# MCQ Questions for Class 12 Maths Chapter 3 Matrices with Answers

Question 1.
$$\left|\begin{array}{lll} 3 & 4 & 5 \\ 0 & 2 & 3 \\ 0 & 0 & 7 \end{array}\right|$$ = A then |A| = ?
(a) 40
(b) 50
(c) 42
(d) 15

Answer

Answer: (c) 42

Question 2.
The inverse of A = $$\left|\begin{array}{ll} 2 & 3 \\ 5 & k \end{array}\right|$$ will not be obtained if A has the value
(a) 2
(b) $$\frac{3}{2}$$
(c) $$\frac{5}{2}$$
(d) $$\frac{15}{2}$$

Answer

Answer: (d) $$\frac{15}{2}$$

Question 3.
For any unit matrix I
(a) I² = I
(b) |I| = 0
(c) |I| = 2
(d) |I| = 5

Answer

Answer: (a) I² = I

Question 4.
A matrix A = [aij]m×n is said to be symmetric if
(a) aij = 0
(b) aij = aji
(c) aij = aij
(d) aij = 1

Answer

Answer: (b) aij = aji

Question 5.
If A = $$\left|\begin{array}{lll} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{array}\right|$$ then A² is
(a) 27 A
(b) 2 A
(c) 3 A
(d) 1

Answer

Answer: (c) 3 A

Question 6.
A matrix A = [aij]m×n is said to be skew symmetric if
(a) aij = 0
(b) aij = aji
(c) aij = -aji
(d) aij = 1

Answer

Answer: (b) aij = aji

Question 7.
A = [aij]m×n is a square matrix if
(a) m = n
(b) m < n
(c) m > n
(d) None of these

Answer

Answer: (a) m = n

Question 8.
If A and B are square matrices then (AB)’ =
(a) B’A’
(b) A’B’
(c) AB’
(d) A’B’

Answer

Answer: (a) B’A’

Question 9.
If A = $$\left[\begin{array}{cc} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{array}\right]$$ and adj A is
(a) $$\left[\begin{array}{cc} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{array}\right]$$
(b) $$\left[\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}\right]$$
(c) $$\left[\begin{array}{cc} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right]$$
(d) $$\left[\begin{array}{cc} -1 & 0 \\ 0 & -1 \end{array}\right]$$

Answer

Answer: (c) $$\left[\begin{array}{cc} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right]$$

Question 10.
If $$\left[\begin{array}{cc} 1-x & 2 \\ 18 & 6 \end{array}\right]$$ = $$\left[\begin{array}{cc} 6 & 2 \\ 18 & 6 \end{array}\right]$$ then x =
(a) ±6
(b) 6
(c) -5
(d) 7

Answer

Answer: (c) -5

Question 11.
If $$\left|\begin{array}{ll} x & 8 \\ 3 & 3 \end{array}\right|$$ = 0, the value of x is
(a) 3
(b) 8
(c) 24
(d) 0

Answer

Answer: (b) 8

Question 12.
If A = $$\left[\begin{array}{cc} i & 0 \\ 0 & i \end{array}\right]$$ then A² =
(a) $$\left[\begin{array}{cc} 1 & 0 \\ 0 & -1 \end{array}\right]$$
(b) $$\left[\begin{array}{cc} -1 & 0 \\ 0 & -1 \end{array}\right]$$
(c) $$\left[\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}\right]$$
(d) $$\left[\begin{array}{cc} -1 & 0 \\ 0 & 1 \end{array}\right]$$

Answer

Answer: (b) $$\left[\begin{array}{cc} -1 & 0 \\ 0 & -1 \end{array}\right]$$

Question 13.
Let A be a non-singular matrix of the order 2 × 2 then |A-1|=
(a) |A|
(b) $$\frac{1}{|A|}$$
(c) 0
(d) 1

Answer

Answer: (b) $$\frac{1}{|A|}$$

Question 14.
If A = $$\left[\begin{array}{cc} 1 & 2 \\ 2 & 1 \end{array}\right]$$ then adj A =
(a) $$\left[\begin{array}{cc} 1 & -2 \\ -2 & 1 \end{array}\right]$$
(b) $$\left[\begin{array}{cc} 2 & 1 \\ 1 & 1 \end{array}\right]$$
(c) $$\left[\begin{array}{cc} 1 & -2 \\ -2 & -1 \end{array}\right]$$
(d) $$\left[\begin{array}{cc} -1 & 2 \\ -2 & -1 \end{array}\right]$$

Answer

Answer: (a) $$\left[\begin{array}{cc} 1 & -2 \\ -2 & 1 \end{array}\right]$$

Question 15.
If A = $$\left[\begin{array}{cc} 1 & 1 \\ 0 & 1 \end{array}\right]$$ B = $$\left[\begin{array}{cc} 0 & 1 \\ 1 & 0 \end{array}\right]$$ then AB =
(a) $$\left[\begin{array}{cc} 0 & 0 \\ 0 & 0 \end{array}\right]$$
(b) $$\left[\begin{array}{cc} 1 & 1 \\ 1 & 0 \end{array}\right]$$
(c) $$\left[\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}\right]$$
(d) 10

Answer

Answer: (b) $$\left[\begin{array}{cc} 1 & 1 \\ 1 & 0 \end{array}\right]$$

Question 16.
If $$\left[\begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ a & b & -1 \end{array}\right]$$ then A² =
(a) a unit matrix
(b) A
(c) a null matrix
(d) -A

Answer

Answer: (a) a unit matrix

Question 17.
If A = $$\left[\begin{array}{cc} α & 0 \\ 1 & 1 \end{array}\right]$$ B = $$\left[\begin{array}{cc} 1 & 0 \\ 5 & 1 \end{array}\right]$$ where A² = B then the value of α is
(a) 1
(b) -1
(c) 4
(d) we cant calculate the value of α

Answer

Answer: (d) we cant calculate the value of α

Question 18.
If A = $$\left[\begin{array}{cc} 1 & 2 \\ 3 & 4 \end{array}\right]$$ then
(a) |A| = 0
(b) A-1 exists
(c) A-1 does not exist
(d) None of these

Answer

Answer: (b) A-1 exists

Question 19.
If A = $$\left[\begin{array}{cc} 2x & 5 \\ 8 & x \end{array}\right]$$ = $$\left[\begin{array}{cc} 6 & -2 \\ 7 & 3 \end{array}\right]$$ then the value of x is
(a) 3
(b) ±3
(c) ±6
(d) 6

Answer

Answer: (a) 3

Question 20.
Let A = $$\left[\begin{array}{cc} 1 & -1 \\ 2 & 3 \end{array}\right]$$ then
(a) A-1 = $$\left[\begin{array}{cc} \frac{3}{5} & \frac{1}{5} \\ \frac{-2}{5} & \frac{1}{5} \end{array}\right]$$
(b) |A| = 0
(c) |A| = 5
(d) A² = 1

Answer

Answer: (a) A-1 = $$\left[\begin{array}{cc} \frac{3}{5} & \frac{1}{5} \\ \frac{-2}{5} & \frac{1}{5} \end{array}\right]$$

Question 21.
If A = $$\left[\begin{array}{ccc} 2 & \lambda & -3 \\ 0 & 2 & 5 \\ 1 & 1 & 3 \end{array}\right]$$ yhen A-1 exists if
(a) λ = 2
(b) λ ≠ 2
(c) λ ≠ -2
(d) none of these

Answer

Answer: (d) none of these

Question 22.
If A = $$\left[\begin{array}{cc} α & 2 \\ 2 & α \end{array}\right]$$ and |A³| = 25 then α is
(a) ±3
(b) ±2
(c) ±5
(d) 0

Answer

Answer: (a) ±3

Question 23.
A² – A + I = 0 then the inverse of A
(a) A
(b) A + I
(c) I – A
(d) A – I

Answer

Answer: (c) I – A

Question 24.
If A = $$\left[\begin{array}{cc} 2 & 3 \\ 1 & -4 \end{array}\right]$$ and B = $$\left[\begin{array}{cc} 1 & -2 \\ -1 & 3 \end{array}\right]$$ then find (AB)-1
(a) $$\frac{1}{11}$$ $$\left[\begin{array}{cc} 14 & 5 \\ 5 & 1 \end{array}\right]$$
(b) $$\frac{1}{11}$$ $$\left[\begin{array}{cc} 14 & -5 \\ -5 & 1 \end{array}\right]$$
(c) $$\frac{1}{11}$$ $$\left[\begin{array}{cc} 1 & 5 \\ 5 & 14 \end{array}\right]$$
(d) $$\frac{1}{11}$$ $$\left[\begin{array}{cc} 1 & -5 \\ -5 & 14 \end{array}\right]$$

Answer

Answer: (a) $$\frac{1}{11}$$ $$\left[\begin{array}{cc} 14 & 5 \\ 5 & 1 \end{array}\right]$$

Question 25.
If A = $$\left[\begin{array}{cc} 3 & 1 \\ -1 & 2 \end{array}\right]$$ then A² – 5A – 7I is
(a) zero matrix
(b) a diagonal matrix
(c) identity matrix
(d) None of these

Answer

Answer: (b) a diagonal matrix

Question 26.
If A = $$\left[\begin{array}{cc} \cos x & -\sin x \\ \sin x & \cos x \end{array}\right]$$ then A + AT = I if the value of x is
(a) $$\frac{π}{6}$$
(b) $$\frac{π}{3}$$
(c) π
(d) 0

Answer

Answer: (b) $$\frac{π}{3}$$

Question 27.
If $$\left[\begin{array}{cc} x+y & y \\ 2x & x-y \end{array}\right]$$ $$\left[\begin{array}{c} 2 \\ -1 \end{array}\right]$$ $$\left[\begin{array}{c} 3 \\ 2 \end{array}\right]$$ then xy equal to
(a) -5
(b) -4
(c) 4
(d) 5

Answer

Answer: (a) -5

Question 28.
If A = $$\left[\begin{array}{cc} 1 & 2 \\ 4 & 2 \end{array}\right]$$ then |2A| =
(a) 2|A|
(b) 4|A|
(c) 8|A|
(d) None of these

Answer

Answer: (b) 4|A|

Question 29.
If A = $$\left[\begin{array}{cc} a & b \\ c & d \end{array}\right]$$ then A² is equal to
(a) $$\left[\begin{array}{cc} a^{2} & b^{2} \\ c^{2} & d^{2} \end{array}\right]$$
(b) $$\left[\begin{array}{cc} b^{2}+bc & ab+bd \\ ac+dc & dc+d^{2} \end{array}\right]$$
(c) $$\left[\begin{array}{cc} a^{3} & b^{3} \\ c^{3} & d^{3} \end{array}\right]$$
(d) None of these

Answer

Answer: (b) $$\left[\begin{array}{cc} b^{2}+bc & ab+bd \\ ac+dc & dc+d^{2} \end{array}\right]$$

Question 30.
$$\left[\begin{array}{cc} \cos \theta & -\sin \theta \\ -\sin \theta & \cos \theta \end{array}\right]$$ is inverse of
(a) $$\left[\begin{array}{cc} -\cos \theta & -\sin \theta \\ -\sin \theta & \cos \theta \end{array}\right]$$
(b) $$\left[\begin{array}{cc} \cos \theta & \sin \theta \\ \sin \theta & -\cos \theta \end{array}\right]$$
(c) $$\left[\begin{array}{cc} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right]$$
(d) None of these

Answer

Answer: (c) $$\left[\begin{array}{cc} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right]$$

Question 31.
A = $$\left[\begin{array}{cc} a & b \\ b & a \end{array}\right]$$ and A² = $$\left[\begin{array}{cc} α & β \\ β & α \end{array}\right]$$ then
(a) α = a² + b², β = ab
(b) α = a² + b², β = 2ab
(c) α = a² + b², β = a² – b²
(d) α = 2ab, β = a² + b²

Answer

Answer: (b) α = a² + b², β = 2ab

Question 32.
The matrix $$\left[\begin{array}{ccc} 2 & -1 & 4 \\ 1 & 0 & -5 \\ -4 & 5 & 7 \end{array}\right]$$ is
(a) a symmetric matix
(b) a skew-sybtmetric matrix
(c) a diagonal matrix
(d) None of these

Answer

Answer: (d) None of these

Question 33.
If a matrix is both symmetric matrix and skew symmetric matrix then
(a) A is a diagonal matrix
(b) A is zero matrix
(c) A is scalar matrix
(d) None of these

Answer

Answer: (b) A is zero matrix

Question 34.
If $$\left[\begin{array}{cc} x+y & 3 \\ 4 & x-y \end{array}\right]$$ = $$\left[\begin{array}{cc} 1 & 3 \\ 4 & -3 \end{array}\right]$$ then (x, y) is
(a) (-1, 2)
(b) (-1, -2)
(c) (-2, -1)
(d) (1, -2)

Answer

Answer: (a) (-1, 2)

Question 35.
The matrix P = $$\left[\begin{array}{ccc} 0 & 0 & 4 \\ 0 & 4 & 0 \\ 4 & 0 & 0 \end{array}\right]$$ is
(a) square matrix
(b) diagonal matrix
(c) unit matrix
(d) None of these

Answer

Answer: (a) square matrix

Question 36.
Total number of possible matrices of order 3 × 3 with each entry 2 or 0 is
(a) 9
(b) 27
(c) 81
(d) 512

Answer

Answer: (d) 512

Question 37.
If $$\left[\begin{array}{cc} 2x+y & 4x \\ 5x-7 & 4x \end{array}\right]$$ = $$\left[\begin{array}{cc} 7 & 7y-13 \\ y & x+6 \end{array}\right]$$ then the value of x, y is
(a) 3, 1
(b) 2, 3
(c) 2, 4
(d) 3, 3

Answer

Answer: (b) 2, 3

Question 38.
If A and B are two matrices of the order 3 × m and 3 × n, respectively, and m = n, then the order of matrix (5A – 2B) is
(a) m × 3
(b) 3 × 3
(c) m × n
(d) 3 × n

Answer

Answer: (d) 3 × n

Question 39.
If A = $$\frac{1}{π}$$ $$\left[\begin{array}{cc} \sin ^{-1}(x \pi) & \tan^{1}\left(\frac{x}{\pi}\right) \\ \sin ^{-1}\left(\frac{x}{\pi}\right) & \cot ^{-1}(\pi x) \end{array}\right]$$
B = $$\frac{1}{π}$$ $$\left[\begin{array}{cc} \cos ^{-1}(x \pi) & \tan ^{-1}\left(\frac{x}{\pi}\right) \\ \sin ^{-1}\left(\frac{x}{\pi}\right) & -\tan ^{-1}(\pi x) \end{array}\right]$$
then A – B equal to
(a) I
(b) O
(c) 1
(d) $$\frac{3}{2}$$ I

Answer

Answer: (d) $$\frac{3}{2}$$ I

Question 40.
If A = $$\left[\begin{array}{cc} 0 & 1 \\ 1 & 0 \end{array}\right]$$ then A² is equal to
(a) $$\left[\begin{array}{cc} 0 & 1 \\ 1 & 0 \end{array}\right]$$
(b) $$\left[\begin{array}{cc} 1 & 0 \\ 1 & 0 \end{array}\right]$$
(c) $$\left[\begin{array}{cc} 0 & 1 \\ 0 & 1 \end{array}\right]$$
(d) $$\left[\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}\right]$$

Answer

Answer: (d) $$\left[\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}\right]$$

Question 41.
If matrix A = [aij]2×2 where aij = {$$_{0 if i = j}^{1 if i ≠ j}$$ then A² is equal to
(a) I
(b) A
(c) O
(d) None of these

Answer

Answer: (a) I

Question 42.
The matrix $$\left[\begin{array}{ccc} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 0 \end{array}\right]$$ is a
(a) identity matrix
(b) symmetric matrix
(c) skew symmetric matrix
(d) None of these

Answer

Answer: (b) symmetric matrix

Question 43.
The matrix $$\left[\begin{array}{ccc} 0 & -5 & 8 \\ 5 & 0 & 12 \\ -8 & -12 & 0 \end{array}\right]$$ is a
(a) diagonal matrix
(b) symmetric matrix
(c) skew symmetric matrix
(d) scalar matrix

Answer

Answer: (c) skew symmetric matrix

Question 44.
If A is matrix of order m × n and B is a matrix such that AB’ and B’A are both defined, then order of matrix B is
(a) m × m
(b) n × n
(c) n × m
(d) m × n

Answer

Answer: (d) m × n

Question 45.
If A and B are matrices of same order, then (AB’ – BA’) is a
(a) skew symmetric matrix
(b) null matrix
(c) symmetric matrix
(d) unit matrix

Answer

Answer: (a) skew symmetric matrix

Question 46.
If A is a square matrix such that A² = I, then (A – I)³ + (A + I)³ – 7A is equal to
(a) A
(b) I – A
(c) I + A
(d) 3 A

Answer

Answer: (a) A

Question 47.
For any two matrices A and B, we have
(a) AB = BA
(b) AB ≠ BA
(c) AB = 0
(d) None of these

Answer

Answer: (d) None of these

Question 48.
If A = [aij]2×2 where aij = i + j, then A is equal to
(a) $$\left[\begin{array}{cc} 1 & 2 \\ 3 & 4 \end{array}\right]$$
(b) $$\left[\begin{array}{cc} 2 & 3 \\ 3 & 4 \end{array}\right]$$
(c) $$\left[\begin{array}{cc} 1 & 1 \\ 2 & 2 \end{array}\right]$$
(d) $$\left[\begin{array}{cc} 1 & 2 \\ 1 & 2 \end{array}\right]$$

Answer

Answer: (b) $$\left[\begin{array}{cc} 2 & 3 \\ 3 & 4 \end{array}\right]$$

Question 49.
The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is
(a) 18
(b) 512
(c) 81
(d) None of these

Answer

Answer: (b) 512

Question 50.
The order of the single matrix obtained from
$$\left[\begin{array}{cc} 1 & -1 \\ 0 & 2 \\ 2 & 3 \end{array}\right]$$ $$\left\{\left[\begin{array}{ccc} -1 & 0 & 2 \\ 2 & 0 & 1 \end{array}\right]-\left[\begin{array}{ccc} 0 & 1 & 23 \\ 1 & 0 & 21 \end{array}\right]\right\}$$ is
(a) 2 × 2
(b) 2 × 3
(c) 3 × 2
(d) 3 × 3

Answer

Answer: (d) 3 × 3

Question 51.
A square matrix A = [aij]n×n is called a diagonal matrix if aij = 0 for
(a) i = j
(b) i < j
(c) i > j
(d) i ≠ j

Answer

Answer: (d) i ≠ j

Question 52.
A square matrix A = [aij]n×n is called a lower triangular matrix if aij = 0 for
(a) i = j
(b) i < j
(c) i > j
(d) None of these

Answer

Answer: (b) i < j

Question 53.
The matrix A = $$\left[\begin{array}{cc} 0 & 1 \\ 1 & 0 \end{array}\right]$$ is a
(a) unit matrix
(b) diagonal matrix
(c) symmetric matrix
(d) skew symmetric matrix

Answer

Answer: (c) symmetric matrix

Question 54.
If $$\left[\begin{array}{cc} x+y & 2x+z\\ x-y & 2z+2 \end{array}\right]$$ = $$\left[\begin{array}{cc} 4 & 7 \\ 0 & 10 \end{array}\right]$$ then find the value of x, y, z and w respectively
(a) 2, 2, 3, 4
(b) 2, 3, 1, 2
(c) 3, 3, 0, 1
(d) None of these

Answer

Answer: (a) 2, 2, 3, 4

Question 55.
If $$\left[\begin{array}{cc} x-y & 2x+z\\ 2x-y & 3z+w \end{array}\right]$$ = $$\left[\begin{array}{cc} -1 & 5 \\ 0 & 13 \end{array}\right]$$ then the value of w is
(a) 1
(b) 2
(c) 3
(d) 4

Answer

Answer: (d) 4

Question 56.
Find x, y, z and w respectively such that
$$\left[\begin{array}{cc} x-y & 2x+z\\ 2x-y & 2x+w \end{array}\right]$$ = $$\left[\begin{array}{cc} 5 & 3 \\ 12 & 15 \end{array}\right]$$
(a) 7, 2, 1, 1
(b) 7, 5, 3, 8
(c) 1, 2, 5, 6
(d) 6, 3, 2, 1

Answer

Answer: (a) 7, 2, 1, 1

Question 57.
If $$\left[\begin{array}{cc} a+b & 2\\ 5 & ab \end{array}\right]$$ = $$\left[\begin{array}{cc} 6 & 2 \\ 5 & 8 \end{array}\right]$$ then find the value of a and b respectively
(a) 2, 4
(b) 4, 2
(c) Both (a) and (b)
(d) None of these

Answer

Answer: (c) Both (a) and (b)

Question 58.
For what values of x and y are the following matrices equal
A = $$\left[\begin{array}{cc} 2x+1 & 3y\\ 0 & y^{2}-5y \end{array}\right]$$ B = $$\left[\begin{array}{cc} x+3 & y^{2}+2 \\ 0 & -6 \end{array}\right]$$
(a) 2, 3
(b) 3, 4
(c) 2, 2
(d) 3, 3

Answer

Answer: (c) 2, 2

Question 59.
If A = $$\left[\begin{array}{cc} α & 0\\ 1 & 1 \end{array}\right]$$ and B = $$\left[\begin{array}{cc} 1 & 0 \\ 5 & 1 \end{array}\right]$$ then find value of α for which A² = B is
(a) 1
(b) -1
(c) 4
(d) None of these

Answer

Answer: (d) None of these

Question 60.
If P = $$\left[\begin{array}{ccc} i & 0 & -i \\ 0 & -i & i \\ -i & i & 0 \end{array}\right]$$ and Q = $$\left[\begin{array}{cc} -i & i \\ 0 & 0 \\ i & -i \end{array}\right]$$ then PQ is equal to
(a) $$\left[\begin{array}{cc} -2 & 2 \\ 1 & -1 \\ 1 & -1 \end{array}\right]$$
(b) $$\left[\begin{array}{cc} 2 & -2 \\ -1 & 1 \\ -1 & 1 \end{array}\right]$$
(c) $$\left[\begin{array}{cc} 2 & -2\\ -1 & 1 \end{array}\right]$$
(d) $$\left[\begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right]$$

Answer

Answer: (b) $$\left[\begin{array}{cc} 2 & -2 \\ -1 & 1 \\ -1 & 1 \end{array}\right]$$

Question 61.
$$\left[\begin{array}{c} 1 & x & 1 \end{array}\right]$$ $$\left[\begin{array}{ccc} 1 & 3 & 2 \\ 2 & 5 & 1 \\ 15 & 3 & 2 \end{array}\right]$$ $$\left[\begin{array}{c} 1 \\ 2 \\ x \end{array}\right]$$
(a) -7
(b) -11
(c) -2
(d) 14

Answer

Answer: (c) -2

Question 62.
If A = $$\left[\begin{array}{cc} 1 & -1\\ 2 & -1 \end{array}\right]$$ B = $$\left[\begin{array}{cc} x & 1\\ y & -1 \end{array}\right]$$ and (A + B)² = A² + B², then x + y is
(a) 2
(b) 3
(c) 4
(d) 5

Answer

Answer: (d) 5

Question 63.
If AB = A and BA = B, then
(a) B = 1
(b)A = I
(c) A² = A
(d) B² = I

Answer

Answer: (c) A² = A

Question 64.
If A = $$\left[\begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ a & b & -1 \end{array}\right]$$ then (A – I) (A + I) = 0 for
(a) a = b = 0 only
(b) a = 0 only
(c) b = 0 only
(d) any a and b

Answer

Answer: (d) any a and b

Question 65.
If A = $$\left[\begin{array}{cc} 1 & 1\\ 0 & 2 \end{array}\right]$$ then A8 – 28 (A – I)
(a) I – A
(b) 2I – A
(c) I + A
(d) A – 2I

Answer

Answer: (b) 2I – A

Question 66.
If A = $$\left[\begin{array}{ccc} 2 & 2 & 1 \\ 1 & 3 & 1 \\ 1 & 2 & 2 \end{array}\right]$$ then A³ – 7A² + 10A =
(a) 5I + A
(b) 5I – A
(c) 5I
(d) 6I

Answer

Answer: (b) 5I – A

Question 67.
If A is a m × n matrix such that AB and BA are both defined, then B is an
(a) m × n matrix
(b) n × m matrix
(c) n × n matrix
(d) m × m matrix

Answer

Answer: (b) n × m matrix

Question 68.
If A = $$\left[\begin{array}{cc} 1 & 2\\ 3 & 4 \end{array}\right]$$ then A2 – 5A is equal to
(a) 2I
(b) 3I
(c) -2I
(d) null matrix

Answer

Answer: (a) 2I

Question 69.
If A = $$\left[\begin{array}{cc} -2 & 4\\ -1 & 2 \end{array}\right]$$ then A2 is
(a) null matrix
(b) unit matrix
(c) $$\left[\begin{array}{cc} 0 & 0\\ 0 & 0 \end{array}\right]$$
(d) $$\left[\begin{array}{cc} 0 & 0\\ 0 & 1 \end{array}\right]$$

Answer

Answer: (a) null matrix

Question 70.
If A and B are 2 × 2 matrices, then which of the following is true?
(a) (A + B)² = A² + B² + 2AB
(b) (A – B)² = A² + B² – 2AB
(c) (A – B)(A + B) = A² + AB – BA – B²
(d) (A + B) (A – B) = A² – B²

Answer

Answer: (c) (A – B)(A + B) = A² + AB – BA – B²