# MCQs For NCERT Class 12 Mathematics Chapter 3 Matrices

Please refer to the MCQ Questions for Class 12 Mathematics Chapter 3 Matrices with Answers. The following Matrices Class 12 Mathematics MCQ Questions have been designed based on the latest syllabus and examination pattern for Class 12. Our experts have designed MCQ Questions for Class 12 Mathematics with Answers for all chapters in your NCERT Class 12 Mathematics book.

## Matrices Class 12 MCQ Questions with Answers

See below Matrices Class 12 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

Question:

(a) B
(b) A
(c) O
(d) I

C

Question:

(a) 20
(b) [- 20]
(c) – 20
(d) 

D

Question:

(a) A
(b) – A
(c) 2A
(d) – 2A

C

Question:  Matrix A has m rows and (n + 5) columns, matrix B has m rows and (11- n) columns. If both AB and BA exist, then
(a) AB and BA are square matrix
(b) AB and BA are of order 8 X 8 and 3X 13  respectively
(c) AB= BA
(d) None of the above

A

Question:

C

Question:

D

Question:

then the values of a and b are respectively
(a) 1, 2
(b) 1, 2
(c) – 1, 2
(d) – 1,- 2

D

Question:

C

Question:

B

Question:  If A

(a) idempotent matrix
(b) involutory matrix
(c) nilpotent matrix
(d) None of these

B

Question:  If A is an orthogonal matrix, then A-1 equals
(a) A
(b) AT
(c) A2
(d) None of these

C

Question:  If A =

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

A

Question: If A is symmetric as well as skew-symmetric matrix, then A is
(a) diagonal matrix
(b) null matrix
(c) triangular matrix
(d) None of these

A

Question:  If A is a skew-symmetric matrix andnis an odd positive integer, then Ais a
(a) symmetric matrix
(b) skew-symmetric matrix
(c) diagonal matrix
(d) None of these

C

Question: If AB = and BA = B, then which of the following is not true?
(a) A is idempotent matrix
(b) B is idempotent matrix
(c) AT is idempotent matrix
(d) None of these

A

Question:  If A is a 3 x 3 skew-symmetric matrix, then trace of A is equal to
(a) – 1
(b) 7
(c) |A|
(d) None of these

C

Question: A skew-symmetric matrix S satisfies the relation S2+ 1= Q, where I is an unitary matrix, then S is an
(a) idempotent matrix
(b) involutory matrix
(c) orthogonal matrix
(d) None of these

C

Question: In which of the following type of matrix there always exists an inverse?
(a) Idempotent matrix
(b) Orthogonal matrix
(c) Involutary matrix
(d) None of these

C

Question: If A,B are two n x n non-singular matrices, then
(a) AB is a non-singular
(b) AB is singular
(c) (AB)-1 = A-B-1
(d) (AB) -1does not exist

A

Question:

A

Question:

A

Question:

B

Question:

C

Question:

C

Question:

(a) 5
(b) 0
(c) 1
(d) None of these

C

Question:

C

Question: If P is non-singular matrix, then the value of ad j (P-1) in terms of P is
(a) P /|p|
(b) P |P|
(c) P
(d) None of these

A

Question: If A and B are two non-singular matrices of the same order such that

(a) I
(b) 2I
(c) 0
(d) -I

C

Question:

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

D

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

D

Question:

B

Question:

D

Question:

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

A

Question:

(a) A
(b) I- A
(c) I +A
(d) 3A

A

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

D

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

D

Question: If A is square matrix such that A2 = A, then (A+I) 3 is equal to
(a) A +1
(b) 7A I +
(c) 3A+ I
(d) A- I

B

Question:

(a) 1
(b) -1
(c) 2
(d) None of these

A

Question:

D

Question:

(a) A
(b) I
(c) I +A
(d) None of the above

C

Question:

A

Question:

equal to
(a) I
(b) 0
(c) -2I
(d) 2I

C

Question:

B

Question. The matrix product

D

Question. Match the terms given in column-I with the terms given in column-II and choose the correct option from the codes given below.

Codes
A B C
(a) 1 2 3
(b) 3 2 1
(c) 2 1 3
(d) 3 1 2

D

Question.

(a) there cannot exist any B such that AB = BA
(b) there exist more than one but finite number of B’s such that AB = BA
(c) there exists exactly one B such that AB = BA
(d) there exist infinitely many B’s such that AB = BA

D

Question.

A

Question.

D

ASSERTION – REASON TYPE QUESTIONS

(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

Question.

Reason: For any square matrix, A (AT)T = A

B

Question.

then B is the inverse of A.
Reason : If A is a square matrix of order m and if there exists another square matrix B of the same order m, such that AB = BA = I, then B is called the inverse of A.

A

Question. Assertion : The possible dimensions of a matrix containing 32 elements is 6.
Reason : The No. of ways of expressing 32 as a product of two positive integers is 6.

C

Question.

Reason : A is not a square matrix.

A

Question.

Reason: A = [aij] is a square matrix such that aij = 0, ∀ i ≠ j, then A is called diagonal matrix.

A

Question. Assertion : The order of the matrix A is 3 × 5 and that of B is 2 × 3. Then the matrix AB is not possible.
Reason : No. of columns in A is not equal to no. of rows in B.

A

Question.

Reason : For the given matrix A we have A’ = A.

C

Question. For any square matrix A with real number entries, consider the following statements.
Assertion : A + A’ is a symmetric matrix.
Reason: A –A’ is a skew-symmetric matrix.

B

Question. Assertion : Addition of matrices is an example of binary operation on the set of matrices of the same order.
Reason: Addition of matrix is commutative.