# 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

Answer

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

Answer

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

Answer

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

Answer

D

Question:

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

Answer

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

Answer

B

Question: The matrix A =

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

Answer

C

Question:

Answer

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

Answer

B

Question:

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

Answer

A

Question:

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

Answer

C

Question: Matrix A =

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

Answer

C

Question:

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

Answer

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

Answer

A

Question:

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

Answer

C

Question:

Answer

C

Question:

(a) 5
(b) 25
(c) –1
(d) 1

Answer

D

Question:

(a) 0
(b) – 1
(c) 1
(d) |A|

Answer

D

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

Answer

B

Question:

(a) A
(b) A’
(c) 3A
(d) 3A

Answer

D

Question:

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

Answer

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

Answer

B

Question.

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

Answer

C

Question.

Answer

B

Question.

Answer

A

Question.

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

Answer

B

Question.

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

Answer

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

Answer

C

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

Answer

B

Question.

Answer

C

Question.

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

Answer

A

Question.

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

Answer

C

Question.

Answer

C

Question.

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

Answer

B

Question.

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

Answer

C

Question.

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

Answer

A

Question.

Answer

C

Question.

(d) none of above

Answer

C

Question.

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

Answer

A

Question.

Answer

B

Question.

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

Answer

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

Answer

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

Answer

D

Question.

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

Answer

D

Question.

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

Answer

A

Question.

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

Answer

C

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

Answer

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

Answer

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

Answer

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

Answer

A

Question.

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

Answer

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

Answer

A

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

Answer

D

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

Answer

D

True/False

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

Answer

False

Question. Matrices of different order cannot be subtracted.

Answer

True

Question. A matrix denotes a number.

Answer

False

Question. Matrices of any order can be added.

Answer

False

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

Answer

False

Question. Matrix multiplication is commutative.

Answer

False

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

Answer

False

Question. Matrix addition is associative as well as commutative.

Answer

True

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

Answer

False

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

Answer

True

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

Answer

False

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

Answer

True

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

Answer

False

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

Answer

True

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

Answer

False

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

Answer

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.

Answer

True

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

Answer

True

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

Answer

True

Question.

Answer

False

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