# Matrices MCQ Questions Class 12 Mathematics

Please refer to MCQ Questions for Class 12 Mathematics Chapter 3 Matrices with answers below. These multiple-choice questions have been prepared based on the latest NCERT book for Class 12 Mathematics. Students should refer to MCQ Questions for Class 12 Mathematics with Answers to score more marks in Grade 12 Mathematics exams. Students should read the chapter Matrices and then attempt the following objective questions.

**MCQ Questions for Class 12 Mathematics Chapter 3 Matrices with answers**

**MCQ Questions for Class 12 Mathematics Chapter 3 **provided below covers all important topics given in this chapter. These MCQs will help you to properly prepare for exams.

**Question. The order of the single matrix obtained from **

(a) 2 × 3

(b) 2 × 2

(c) 3 × 2

(d) 3 × 3

**Answer**

D

**Question. **

**Answer**

C

**Question. **

**then x =**

(a) 2

(b) 3

(c) 4

(d) 5

**Answer**

D

**Question. If A is a square matrix, then AA’ is a**

(a) skew-symmetric matrix

(b) symmetric matrix

(c) diagonal matrix

(d) None of these

**Answer**

B

**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

**Question. What is true about matrix multiplication ?**

(a) It is commutative.

(b) It is associative.

(c) Both of the above.

(d) None of the above.

**Answer**

B

**Question. If A = [a _{ij}] is a matrix of order 4 × 5, then the diagonal elements of A are**

(a) a

_{11}, a

_{22}, a33, a

_{44}

(b) a

_{55}, a

_{44}, a

_{33}, a

_{22}, a

_{11}

(c) a

_{11}, a

_{22}, a

_{33}

(d) do not exist

**Answer**

D

**Question. If A is symmetric as well as skew-symmetric matrix, then A is**

(a) Diagonal

(b) Null

(c) Triangular

(d) None of these

**Answer**

B

**Question. 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**

B

**Question.**

**then, the values of a, b, c, x, y and z respectively are**

(a) – 2, – 7, – 1, – 3, – 5, – 2

(b) 2, 7, 1, 3, 5, – 2

(c) 1, 3, 4, 2, 8, 9

(d) – 1, 3, –2, –7, 4, 5

**Answer**

A

**Question. **

**Answer**

A

**Question. Choose the incorrect statement.**

(a) A matrix A = [3] is a scalar matrix of order 1

(d) None of the above

**Answer**

C

**Question. The matrix X such that**

**Answer**

B

**Question.**

(a) R (s + t)

(b) R (s – t)

(c) R(s) + R(t)

(d) None of these

**Answer**

A

**Question. **

(a) symmetric

(b) diagonal

(c) upper triangular

(d) skew symmetric

**Answer**

C

**Question. If A is any square matrix, then which of the following is skew-symmetric?**

(a) A + A^{T}

(b) A – A^{T} (c) AA^{T}

(d) A^{T}A

**Answer**

B

**Question. **

**Answer**

A

**Question.**

**then the values of x, y, z and w respectively** are

(a) 2, 2, 3, 4

(b) 2, 3, 1, 2

(c) 3, 3, 0, 1

(d) None of these

**Answer**

A

**Question.**

**Answer**

B

**Question. **

**then n =**

(a) 2

(b) 3

(c) 4

(d) 5

**Answer**

A

**Question. If A is a m ×n matrix with entries aij, then the matrix A can be represented as**

(a) A = [a_{ij}]_{m × n}

(b) A = [a_{ji}]_{m × n}

(c) A = [a_{ij}]_{n × m}

(d) A = [a_{ji}]_{n × m }

**Answer**

A

**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) 2 1 3

(b) 3 2 1

(c) 3 1 2

(d) 1 3 2

**Answer**

C

**Question. If A = [aij]m × n, then A’ is equal to**

(a) [a_{ji}]_{n × m}

(b) [a_{ij}]_{m × n}

(c) [a_{ji}]_{m × n}

(d) [a_{ij}]_{n × m }

**Answer**

A

**Question. Using elementary transformation, the inverse of the matrix**

**Answer**

C

**Question. If A, B are two square matrices such that AB = A and BA = B, then**

(a) only B is idempotent

(b) A, B are idempotent

(c) only A is idempotent

(d) None of these

**Answer**

B

**Question. **

(a) I + A

(b) I – A

(c) A – I

(d) A

**Answer**

A

**Question. Let A and B be two matrices then (AB)’ equals:**

(a) B’A’

(b) A’B

(c) – AB

(d) 1

**Answer**

A

**Question. **

(a) AB, BA exist and are equal

(b) AB, BA exist and are not equal

(c) AB exists and BA does not exist

(d) AB does not exist and BA exists

**Answer**

B

**Question. If A is a matrix having m rows and n columns, then the matrix A is called a matrix of order**

(a) m × n

(b) n × m

(c) mn

(d) nm

**Answer**

A

**Question. Let A = [a _{ji}] be an m × n matrix and B = [b_{jk}] be an n × p matrix. Then, the product of the matrices A and B is the matrix C of order.**

(a) n × m

(b) m × n

(c) p × m

(d) m × p

**Answer**

D

**Question. If A is a square matrix of order m, then the matrix B of same order is called the inverse of the matrix A, if**

(a) AB = A

(b) BA = A

(c) AB = BA = I

(d) AB = –BA

**Answer**

C

**Question. **

(a) 4A

(b) 3A

(c) 2A

(d) A

**Answer**

B

**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 D

(a) 2 3 1 4

(b) 4 3 2 1

(c) 3 4 1 2

(d) 3 1 4 2

**Answer**

B

**Question. For any square matrix A, AA ^{T} is a**

(a) unit matrix

(b) symmetric matrix

(c) skew-symmetric matrix

(d) diagonal matrix

**Answer**

B

**Question. **

**then y =**

(a) 6

(b) 1

(c) 8

(d) 9

**Answer**

A

**Question. The matrix C = [c _{ik}]_{m × p} is the product of A = [a_{ij}]_{m × n} and B = [b_{jk}]_{n × p} where c_{ik} is**

**Answer**

C

**Question. If A is a square matrix such that A ^{2} = 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 the diagonal elements of a diagonal matrix are all equal, then the matrix is called**

(a) row matrix

(b) scalar matrix

(c) rectangular matrix

(d) None of the above

**Answer**

B

**Question. If ω is a complex cube root of unity, then the matrix**

(a) symmetric matrix

(b) diagonal matrix

(c) skew-symmetric matrix

(d) None of these

**Answer**

A

**Question. **

**then value of B in terms of I and J is**

(a) Isin θ + J cosθ

(b) Isin θ – J cosθ

(c) Icos θ + J sin θ

(d) –Isin θ + J cos θ

**Answer**

C

**Question.**

** then the values of k, a, b are respectively.**

(a) –6, –12, –18

(b) –6, 4, 9

(c) –6, –4, –9

(d) –6, 12, 18

**Answer**

C

**Question. **

**Answer**

D

**Question. A square matrix A = [a _{ij}]_{n×n} is called a lower triangular matrix if a_{ij} = 0 for**

(a) i = j

(b) i < j

(c) i > j

(d) None of these

**Answer**

B

**STATEMENT TYPE QUESTIONS**

**Question. Consider the following statements****I. For multiplication of two matrices A and B, the number of columns in A should be less than the number of rows in B.****II. For getting the elements of the product matrix, we take rows of A and column of B, multiply them elementwise and take the sum.****Choose the correct option.**

(a) Only I is true

(b) Only II is true

(c) Both I and II are true

(d) Neither I nor II is true

**Answer**

B

**Question. Consider the following statements**

**where k is a scalar, in an identity matrix when k = 1.****II. Every identity matrix is not a scalar matrix.****Choose the correct option.**

(a) Only I is true

(b) Only II is true

(c) Both I and II are true

(d) Both I and II are false

**Answer**

A

**Question. **

**Now, consider the following statements****I. The order of the matrix is 4 × 3 and number of elements is 12.****II. The elements a _{13}, a_{21}, a_{33} are respectively19, 35, –5.**

**Choose the correct option.**

(a) Only I is true

(b) Only II is true

(c) Both I and II are true

(d) Neither I nor II is true

**Answer**

B

**Question. Let A, B and C are three matrices of same order. Now, consider the following statements****I. If A = B, then AC = BC****II. If AC = BC, then A = B****Choose the correct option**

(a) Only I is true

(b) Only II is true

(c) Both I and II are true

(d) Neither I nor II is true

**Answer**

A

**Question. Consider the following statements.****I. If a matrix has 24 elements, then all the possible orders it can have are 24 × 1, 1 × 24, 2 × 4, 4 × 2, 2 × 12, 12 × 2, 3 × 8, 8 ×3, 4 ×6 and 6 × 4.****II. For a matrix having 13 elements, its all possible orders are 1 × 13 and 13 × 1.****III. For a matrix having 18 elements, its all possible orders are 18 × 1, 1 × 18, 2 × 9, 9 × 2, 3 × 6, 6 × 3.****IV. For a matrix having 5 elements, its all possible orders are 1 × 5 and 5 × 1.****Choose the correct option**

(a) Only I is false

(b) Only II is a false

(c) Only III is false

(d) All are true

**Answer**

A

**Question. Consider the following statements****I. If AB and BA are both defined, then they must be equal i.e., AB = BA.****II. If AB and BA are both defined, it is not necessary that AB = BA.****Choose the correct option.**

(a) Only I is true

(b) Only II is true

(c) both I and II are true

(d) None of these

**Answer**

B

**Question. **

**Consider the following statements****I. The matrices A, B and C are diagonal matrices.****II. The matrices A, B and C are of order 1, 3 and 2, respectively.****Choose the correct option.**

(a) I is true and II is false

(b) I is false and II is true

(c) Both I and II are true

(d) Both I and II are false

**Answer**

A