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

Question

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, 5, 10, 15, 16

MARKS App · Accepted Answer

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 ⇒ A = A 16 ⇒ A 15 = I

Search any question & find its solution

Looking for more such questions to practice?