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NCERT Solutions for class 12 Maths | Chapter 3 - Matrices

(1) If A = then find value of α for which A² = B is
[A] 1
[B] -1
[C] 4
[D] None of these
Answer: None of these
(2) If A = then A8 – 28 (A – I)
[A] I – A
[B] A
[C] I + A
[D] A – 2I
Answer: 2I – A

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(3) If A = then A2 – 5A is equal to
[A] 2I
[B] 3I
[C] -2I
[D] null matrix
Answer: 2I
(4) If A =

B =

then A – B equal to

[A] I
[B] O
[C] 1
[D] 3/2 |
Answer: 3/2 |
(5) If then find the value of x, y, z and w respectively
[A] 2, 2, 3, 4
[B] 2, 3, 1, 2
[C] 3, 3, 0, 1
[D] None of these
Answer: 2, 2, 3, 4
(6) If A = then the value of x is
[A] 3
[B] ±3
[C] ±6
[D] 6
Answer: 3
(7) If A = then A² – 5A – 7I is
[A] zero matrix
[B] a diagonal matrix
[C] identity matrix
[D] None of these
Answer: a diagonal matrix
(8) If A = then |2A| =
[A] 2|A|
[B] 4|A|
[C] 8|A|
[D] None of these
Answer: 4|A|
(9)
[A] α = a² + b², β = ab
[B] α = a² + b², β = 2ab
[C] α = a² + b², β = a² – b²
[D] α = 2ab, β = a² + b²
Answer: α = a² + b², β = 2ab
(10) If then the value of x, y is
[A] 3, 1
[B] 2, 3
[C] 2, 4
[D] 3, 3
Answer: 2, 3
(11) If P is of order 2 x 3 and Q is of order 3 x 2, then PQ is of order
[A] 2 x 3
[B] 2 x 2
[C] 3 x 2
[D] 3 x 3
Answer: 2 x 2
(12) If a matrix has 24 elements then the number of possible order it can have, is
[A] 6
[B] 8
[C] 12
[D] 16
Answer: 8
(13) If A and B are two matrices such that both AB and BA are defined, then
[A] A and B can be any two matrices .
[B] A and B are not square matrices not necessarily of the same order.
[C] A and B are square matrices of the same order .
[D] number of columns of A = number of rows of B .
Answer: A and B are not square matrices not necessarily of the same order.
(14) If A is an orthogonal matrix then AT is a/an
[A] identity matrix
[B] null matrix
[C] orthogonal matrix
[D] scalar matrix
Answer: orthogonal matrix
(15) If A = [3 4 7 -1] [1 6 7 2] [9 8 6 4]

then the order of the matrix is

[A] 4 * 3
[B] 3 * 4
[C] 3 * 3
[D] 4 * 4
Answer: 3 * 4
(16) If 2[3 4] + [1 y] = [7 0] [5 x] [0 1] [10 5] then the value of x - y is
[A] 8
[B] 10
[C] -8
[D] -10
Answer: 10
(17) If A = [ 2 -3 -1 4] then the matrix B such that 2A + 3B = 0 is
[A] [4/3 2 2/3 -8/3]
[B] [-4/3 2 2/3 8/3]
[C] [-4/3 2 2/3 -8/3]
[D] [-4/3 2 -2/3 -8/3]
Answer: [-4/3 2 2/3 -8/3]
(18) If A is a skew symmetric matrix of order 3, then the value of determinant A is
[A] 0
[B] 1
[C] -1
[D] None of these
Answer: 0
(19) If A is a square matrix, then A is symmetric iff
[A] A2 = A
[B] A2 = I
[C] At = A
[D] At = - A
Answer: At = A
(20) If A is any square matrix, then
[A] A + At is symmetric
[B] A - At is symmetric
[C] AAt is scew symmetric
[D] none of these
Answer: A + At is symmetric

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