Let A and B be two non singular matrices of same order such that A B k = A k B k for consecutive positive integral values of k , then A B 2 A - 1 is equal to

Question

Let A and B be two non singular matrices of same order such that A B k = A k B k for consecutive positive integral values of k , then A B 2 A - 1 is equal to, A 2, B, A, B 2

MARKS App · Accepted Answer

A ≠ 0 , B ≠ 0 (given) A B 3 = A 3 B 3 … i Also, A B 3 = A B 2 A B = A 2 B 2 A B … i i From i and i i A B 2 = B 2 A A B 2 A - 1 = B 2 A A - 1 = B 2

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