NCERT Solutions : Class 12 Maths with Answers MCQs Chapter 3

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.

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