Q47 / 75 · NTA Abhyas (JEE Main) 2020 · Mathematics · Matrices

Let $A$ and $B$ are two non-singular matrices such that $A B = B A^{2}, B^{4} = I$ and $A^{k} = I,$ then $k$ can be equal to

A
$5$
B
$10$
Correct answer
C
$15$
D
$16$

Solution

A B^{4} = A B (B) (B) (B)

= B A^{2} (B) (B) (B)

= B A (A B) B B

= B A (B A^{2}) B B

= B (A B) (A^{2} B B)

= B B A^{4} B B

= B^{2} B A^{8} B = B^{4} A^{16}

\Rightarrow A = A^{16} \Rightarrow A^{15} = I

Hence, the correct answer is option: 'C'.

More Matrices Questions

Let A be a non-singular symmetric matrix of order 3 . If A T = A 2 - I , then A - I - 1 is equal to
If A = 1 1 3 5 2 6 - 2 - 1 - 3 , where A x = O (where, O is a null matrix and x 15 , x ∈ N ), then which of the following is true?
If A 1 , A 2 , A 3 … … . A 20 are 20 skew-symmetric matrices of same order and B = ∑ r = 1 20 2 r A r 2 r + 1 , then the sum of the principa
If P = λ 0 1 1 and Q = 4 0 3 1 such that P 2 = Q , then P 3 is equal to
Consider A = a 11 a 12 a 21 a 22 and B = 1 1 2 1 such that A B = B A , then the value of a 12 a 21 + a 11 a 22 is
Let A = 1 2 3 4 and B = p q r s are two matrices such that A B = B A and r 0 , then the value of 3 p - 3 s 5 q - 4 r is equal to