# NCERT Solutions : Class 12 Maths with Answers MCQs Chapter 3

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

NCERT Books are textbooks which are issued & distributed by the National Council of Educational Research and Training (NCERT). NCERT books are important for the schooling system. NCERT Books are available in E-Books. If you are searching for MCQs (Multiple Choice Questions) with Answers of for NCERT Class 12 Mathematics then you have came to right way. CBSE students can also solve NCERT Class 12 Maths Chapter 3 Matrices PDF Download w their preparation level. MCQs are Prepared Based on Latest Exam Patterns. MCQs Questions with Answers for Class 12 Maths Chapter 3 Matrices are prepared to help students to understand concepts very well. Objective wise Questions 12th class Maths Chapter 3 Matrices wise PDF over here are available in the following links. Score maximum marks in the exam.

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

(a) 2
(b) 4
(c) 3
(d) 6

Option b – 4

(a) 6
(b) 36
(c) 32
(d) 64

Option d – 64

(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

(a) I – A
(b) A – I
(c) A
(d) A + I

Option a – I – A

(a) 9
(b) 27
(c) 81
(d) 512

Option d – 512

(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

(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

(a) m × 3
(b) 3 × 3
(c) m × n
(d) 3 × n

Option d – 3 × n

(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

(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.