NCERT Solutions for class 12 Maths | Chapter 3 - Matrices

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Questions
1 If A is a m × n matrix such that AB and BA are both defined, then B is an
A m × n matrix
B n × m matrix
C n × n matrix
D m × m matrix

Answer:n × n matrix
2 If AB = A and BA = B, then
A B = 1
B A = I
C A² = A
D B² = I

Answer:A² = A
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3 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

Answer:i < j
4 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:512
5 For any two matrices A and B, we have
A AB = BA
B AB ≠ BA
C AB = 0
D None of these

Answer:None of these
6 If A is a square matrix such that A² = I, then (A – I)³ + (A + I)³ – 7A is equal to
A A
B I – A
C I + A
D 3 A

Answer:A
7 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

Answer:m × n
8 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:3 × n
9 For any unit matrix I
A I² = I
B |I| = 0
C |I| = 2
D |I| = 5

Answer:I² = I
10 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

Answer:aij = aji
11 If A and B are square matrices then (AB)’ =
A B’A’
B A’B’
C AB’
D A’B’

Answer:B’A’
12 Let A be a non-singular matrix of the order 2 × 2 then |A-1|=
A |A|
B 1/|A|
C 0
D 1

Answer:1/|A|
13 If A = Matrices then
A |A| = 0
B A-1 exists
C A-1 does not exist
D None of these

Answer:A-1 exists
14 A² – A + I = 0 then the inverse of A
A A
B A + I
C I – A
D A – I

Answer:I – A
15 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

Answer:A is zero matrix
16 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:512
17 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

Answer:skew symmetric matrix
18 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

Answer:i ≠ j
19 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

Answer:(A – B)(A + B) = A² + AB – BA – B²
20 A = [aij]m×n is a square matrix if
A m = n
B m < n
C m > n
D None of these

Answer:m = n

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