## NCERT Solutions for Class 12 Maths Chapter 3 MCQ’s with Answers

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## NCERT **Maths MCQs for Class 12 Question and Answers Chapter 4 Determinants PDF**

### Q1. If a matrix has 6 elements, then number of possible orders of the matrix can be

(a) 2

(b) 4

(c) 3

(d) 6

Option b – 4

### Q2. Total number of possible matrices of order 2 × 3 with each entry 1 or 0 is

(a) 6

(b) 36

(c) 32

(d) 64

Option d – 64

### Q3. If A is a square matrix such that A²=A, then (I + A)² – 3A is

(a) I

(b) 2A

(c) 3I

(d) A

Option a -I

### Q4. If matrices A and B are inverse of each other then

(a) AB = BA

(b) AB = BA = I

(c) AB = BA = 0

(d) AB = 0, BA = I

Option d – AB = 0, BA = I

### Q5. If a matrix A is both symmetric and skew symmetric then matrix A is

(a) a scalar matrix

(b) a diagonal matrix

(c) a zero matrix of order n × n

(d) a rectangular matrix.

Option c – a zero matrix of order n × n

### Q6. Show that the matrix B’AB is symmetric or skew symmetric according as A is symmetric or skew symmetric.

Option Let A is symmetric then A’ = A …(i) Now (B’AB)’ = B’A'(B’)’ = B’A’B = B’AB [using (i)] Hence, symmetric. Similarly, let A be skew symmetric then A’= -A (B’AB)’ = B’A'(B’)’ = B’A’B = B'(-A)B = -B’AB. Hence, B’AB is skew symmetric.

### Q7. If A and B are symmetric matrices of the same order, then

(a) AB is a symmetric matrix

(b) A – Bis askew-symmetric matrix

(c) AB + BA is a symmetric matrix

(d) AB – BA is a symmetric matrix

Option c – AB + BA is a symmetric matrix

### Q8. If A is a square matrix, then A – A’ is a

(a) diagonal matrix

(b) skew-symmetric matrix

(c) symmetric matrix

(d) none of these

Option b – skew-symmetric matrix

### Q9. If A is any square matrix, then which of the following is skew-symmetric?

(a) A + AT

(b) A – AT

(c) AAT

(d) ATA

Option b – A – AT

### Q10. If A2 – A + I = O, then the inverse of A is

(a) I – A

(b) A – I

(c) A

(d) A + I

Option a – I – A

### Q11. Total number of possible matrices of order 3 × 3 with each entry 2 or 0 is

(a) 9

(b) 27

(c) 81

(d) 512

Option d – 512

### Q12. If A is a matrix of order m × n and B is a matrix such that AB’ and B’A are both defined, then the order of matrix B is

(a) m × m

(b) n × n

(c) n × m

(d) m × n

Option d – m × n

### Q13. For any unit matrix I

(a) I² = I

(b) |I| = 0

(c) |I| = 2

(d) |I| = 5

Option a – I² = I

### Q14. A matrix A = [aij]m×n is said to be skew symmetric if

(a) aij = 0

(b) aij = aji

(c) aij = -aji

(d) aij = 1

Option b – aij = aji

### Q15. If A and B are square matrices then (AB)’ =

(a) B’A’

(b) A’B’

(c) AB’

(d) A’B’

Option a – B’A’

### Q16. If a matrix is both symmetric matrix and skew symmetric matrix then

(a) A is a diagonal matrix

(b) A is zero matrix

(c) A is scalar matrix

(d) None of these

Option b – A is zero matrix

### Q17. 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

Option d – 3 × n

### Q18. If A is matrix of order m × n and B is a matrix such that AB’ and B’A are both defined, then order of matrix B is

(a) m × m

(b) n × n

(c) n × m

(d) m × n

Option d – m × n

**Q19**. 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

Option a – skew symmetric matrix

### Q20. For any two matrices A and B, we have

(a) AB = BA

(b) AB ≠ BA

(c) AB = 0

(d) None of these

Option d – None of these

### Q21. A square matrix A = [aij]n×n is called a diagonal matrix if aij = 0 for

(a) i = j

(b) i < j

(c) i > j

(d) i ≠ j

Option d – i ≠ j

### Q22. A square matrix A = [aij]n×n is called a lower triangular matrix if aij = 0 for

(a) i = j

(b) i < j

(c) i > j

(d) None of these

Option b – i < j

### Q23. If AB = A and BA = B, then

(a) B = 1

(b)A = I

(c) A² = A

(d) B² = I

Option c – A² = A

### Q24. If A and B are 2 × 2 matrices, then which of the following is true?

(a) (A + B)² = A² + B² + 2AB

(b) (A – B)² = A² + B² – 2AB

(c) (A – B)(A + B) = A² + AB – BA – B²

(d) (A + B) (A – B) = A² – B²

Option c – (A – B)(A + B) = A² + AB – BA – B²

### Q25. For any square matrix A, AAT is a

(a) unit matrix

(b) symmetric matrix

(c) skew-symmetric matrix

(d) diagonal matrix

Option b – symmetric matrix

We hope that the given** NCERT MCQ** **Questions for Class 12 Mathematics Chapter 3 Matrices** **Free Pdf download** will help you in gaining knowledge on the subject.