# MCQ Questions Chapter 3 Matrices Class 12 Mathematics

Please refer to MCQ Questions Chapter 3 Matrices Class 12 Mathematics with answers provided below. These multiple-choice questions have been developed based on the latest NCERT book for class 12 Mathematics issued for the current academic year. We have provided MCQ Questions for Class 12 Mathematics for all chapters on our website. Students should learn the objective based questions for Chapter 3 Matrices in Class 12 Mathematics provided below to get more marks in exams.

## Chapter 3 Matrices MCQ Questions

Question. If A= [aij] mxn and B= [bij]pxq and AB= BA then
(a) n=p
(b) n=p, m=n
(c) m=n=p=q
(d) m=q

C

Question: 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

A

Question: If a, b and c are all different from zero such that 1/a +1/b +1/c=0,   then the matrix
(a) symmetric
(b) non-singular
(c) can be written as sum of a symmetric and a skew-symmetric matrix
(d) All of the above

D

Question: For what value of x, the matrix

is singular
(a) x = 1, 2
(b) x = 0, 2
(c) x = 0, 1
(d) x = 0 ,3

D

Question:

(a) 4
(b) 3
(c) -4
(d) -3

C

Question: For any 2x 2  matrix A, if A (a d j A) =

then |A | is equal to
(a) 0
(b) 10
(c) 20
(d) 100

B

Question: The matrix A =

is
(a) unitary
(b) orthogonal
(c) nilpotent
(d) involutory

C

Question:

A

Question: If A is a singular matrix, then A adj (A )
(a) is a scalar matrix
(b) is a zero matrix
(c) is an identity matrix
(d) is an orthogonal matrix

B

Question:

(a) A is singular
(b) | | A ¹ 0
(c) A is symmetric
(d) None of these

A

Question:

(a) A
(b)| A|
(c) |A | I
d) None of these

C

Question: Matrix A =

is invertible for
(a) k = 1
(b) k = – 1
(c) k = ± 1
(d) None of these

C

Question:

(a) A
(b) |A|
(c) |A|I
(d) None of these

A

Question: If A is a skew-symmetric matrix of odd order, then A| is equal to
(a) 0
(b) n
(c) n2
(d) None of these

A

Question:

(a) 124
(b) 134
(c) 144
(d) None of these

C

Question:

C

Question:

(a) 5
(b) 25
(c) –1
(d) 1

D

Question:

(a) 0
(b) – 1
(c) 1
(d) |A|

D

Question: If A2– A+I = 0, then the inverse of A is
a) A- I
(b) I- A
(c) A + 1
(d) A

B

Question:

(a) A
(b) A’
(c) 3A
(d) 3A

D

Question:

(a) – 1 6
(b) 1/ 3
(c) – 1/ 3
(d) 1/ 6

A

Question. If A is of order 2x3 and B is of order 3x2, then the order of AB is :
(a) 3x3
(b) 2x2
(c) 3x2
(d) 2x3

B

Question.

(a) 5A
(b) 10A
(c) 16 A
(d) 32 A

C

Question.

B

Question.

A

Question.

(a) (3,7)
(b) (9,14)
(c) (5,14)
(d) (3,14)

B

Question.

(a) I
(b) 2I
(c) 3I
(d) 4A

B

Question. If A is a square matrix , then AAT + ATA is :
(a) Unit matrix
(b) null matrix
(c) symmetric matrix
(d) skew-symmetric matrix

C

Question. If aij= i + j then A = [𝑎𝑖𝑗]3×4 is :

B

Question.

C

Question.

(a) (2,4), (4,2)
(b) (3,3),(3,4)
(c) (2,2),(1,1)
(d) none of above

A

Question.

(a) 1
(b) 2
(c) 1/2
(d) -2

C

Question.

C

Question.

(a) -5
(b) -1/5
(c) 1/25
(d) 25

B

Question.

(a) a = 2, b = -3
(b) a = -2, b = -3
(c) a = 1, b = 4
(d) none of above

C

Question.

(a) 0
(b) I2
(c) -I2
(d) none of these

A

Question.

C

Question.

(d) none of above

C

Question.

(a) 1/3
(b) 5
(c) 3
(d) 1

A

Question.

B

Question.

(a) x = 3,y =1
(b) x = 2,y = 3
(c) x = 2,y = 4
(d) x = 3,y = 3

B

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

A

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

D

Question.

(a) I
(b) 0
(c) 2I
(d) (1/2)I

D

Question.

(a) square matrix
(b) diagonal matrix
(c) unit matrix
(d) None of these

A

Question.

(a) diagonal matrix
(b) symmetric matrix
(c) skew-symmetric matrix
(d) scalar matrix

C

Question. On using elementary row operation R1  R1 – 3R2 in the following

A

Question. 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) 3A

A

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

D

Question. If matrix A  =[ aij ]2×2, where aij = 1, if i ≠ j = 0 and if i = j, then A2 is equal to
(a) I
(b) A
(c) 0
(d) None of these

A

Question.

(a) identity matrix
(b) symmetric matrix
(c) skew-symmetric matrix
(d) None of these

B

Question. 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

A

Question. On using elementary column operations C2 → C2 – 2C1 in the

D

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

D

True/False

Question. Two matrices are equal, if they have same number of rows and same number of columns.

False

Question. Matrices of different order cannot be subtracted.

True

Question. A matrix denotes a number.

False

Question. Matrices of any order can be added.

False

Question. If matrix AB = 0, then A = 0 or B = 0 or both A and B are null matrices.

False

Question. Matrix multiplication is commutative.

False

Question. A square matrix where every element is unity is called an identity matrix.

False

Question. Matrix addition is associative as well as commutative.

True

Question. If A and B are two matrices of the same order, then A – B = B – A.

False

Question. If A and B are two square matrices of the same order, then A + B = B + A.

True

Question. If A, B and C are square matrices of same order, then AB = AC always implies that B = C.

False

Question. If each of the three matrices of the same order are symmetric, then their sum is a symmetric matrix.

True

Question. If A and B are any two matrices of the same order, then (AB)’ = A’B’.

False

Question. If A is skew-symmetric matrix, then A2 is a symmetric matrix.

True

Question. Transpose of a column matrix is a column matrix.

False

Question. If A and B are two square matrices of the same order, then AB = BA.

False

Question. If (AB)’ = B’ A’, where A and B are not square matrices, then number of rows in A is equal to number of columns in B and number of columns in A is equal to number of rows in B.

True

Question. (AB)-1 = A-1 · B-1, where A and B are invertible matrices satisfying commutative property with respect to multiplication.

True

Question. AA’ is always a symmetric matrix for any matrix A.