**MCQs Questions for Class 12 Maths Chapter 3 Matrices**

In this 21^{st} century, Multiple Choice Questions (MCQs) play a vital role to prepare for a competitive examination. CBSE board has also brought a major change in its board exam patterns.

In most of the competitive examinations, only MCQ questions are asked. So, for getting ready for the competitive examinations, we have to practice for MCQ questions to solve. It strengthens the critical thinking and problem solving skills.

In future, if you want to prepare for competitive examination and to crack it, then you should more focus on the MCQ questions. Thus, from the board examinations point of view and competitive examinations point of view, you should practice more on multiple choice questions.

Thus, let’s solve these MCQs Questions to make our foundation very strong.

**MCQs Questions for Class 12 Maths Chapter 3 Matrices**

**1.** If the order of a
matrix is m × n, then the number of elements in the matrix is

(a) mn^{2}

(b) m^{2} n^{2}

(c) mn

(d) 2mn

**Answer:**** c**

**2. **If A and B are symmetric
matrices of the same order, then

(a) AB is a
symmetric matrix

(b) A – B is
a skew-symmetric matrix

(c) AB + BA
is a symmetric matrix

(d) AB – BA
is a symmetric matrix

**Answer: c**

**3. **A matrix A = [a_{ij}]_{m×n} is
said to be symmetric matrix, if

(a) a_{ij} =
0

(b) a_{ij} =
a_{ji}

(c) a_{ij} =
a_{ij}

(d) a_{ij} =
1

**Answer:**** b**

**4. **If A is a square matrix, then A – A’ is a

(a)
diagonal matrix

(b)
symmetric matrix

(c) skew-symmetric
matrix

(d) none of
these

**Answer: c **

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

(a) A + A^{T}

(b) A – A^{T}

(c) AA^{T}

(d) A^{T}A

**Answer: b**

**6. **The matrix which follows
the conditions m = n is called a

(a) Square
matrix

(b)
Rectangular matrix

(c) Scalar
matrix

(d)
Diagonal matrix

**Answer:**** a**

**7. **A matrix A = [a_{ij}]_{m×n} is said to
be skew-symmetric matrix, if

(a) a_{ij} =
0

(b) a_{ij} =
a_{ji}

(c) a_{ij} =
-a_{ji}

(d) a_{ij} =
1

**Answer:**** b**

**8. **If A^{2} – A + I = O, then the inverse of A is
equal to

(a) I – A

(b) A – I

(c) A

(d) A + I

**Answer: a**

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

(a) unit
matrix

(b)
symmetric matrix

(c) skew-symmetric
matrix

(d)
diagonal matrix

**Answer: b**

**10. **Which of the following
conditions is not correct for matrix multiplication?

(a) A(BC) =
(AB)C

(b) A(B+C) =
AB+AC

(c) AB = 0
if either A or B is 0

(d) AB = BA

**Answer:**** d**

**11. **If A and B are square matrices, then (AB)’ is equal to

(a) B’A’

(b) A’B’

(c) AB’

(d) A’B’

**Answer:**** a**

**12. **The 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: d**

**13. **If a matrix A is both
symmetric and skew-symmetric, then

(a) A is a
diagonal matrix

(b) A is a
zero matrix

(c) A is a
scalar matrix

(d) A is a
square matrix

**Answer: b**

**14. **Which of the following
conditions holds true for a skew-symmetric matrix?

(a) A = IA

(b) A = |A|

(c) A = A’

(d) A = -A’

**Answer:**** a**

**15. **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:**** d**