Question

A and B are square matrices and A is non-singular matrix, (A–1BA)n, n Ī I+, is equal to

• A. A–nBnAn
• B. AnBnA–n
• C. A–1BnA
• D. A–nBAn

Answer 1

Answer: (C)

A–1BnA

Answer 2

For n = 2 Ž(A–1 BA) (A–1BA) = A–1B2A

(A–1 BA)3 = (A–1BA)2 (A–1BA) = (A–1B2A) (A–1BA)

= A–1B3A and so on thus (A–1BA)n = A–1BnA