Question

If A and B are square matrices of the same order and A is non-singular then for a positive integer n, (A^–1BA)ⁿ is equals

• A. AⁿBⁿA^–n
• B. A^–1BⁿA
• C. A^–nBⁿAⁿ
• D. n(A^–1BA)

Answer 1

Answer: (B)

A^–1BⁿA

Answer 2

(A^–1 B A)ⁿ

=A^–1B$\begin{matrix} A.A^{–1} \end{matrix}$B$\begin{matrix} A.A^{–1} \end{matrix}$B$\begin{matrix} A.A^{–1} \end{matrix}$B A...A^–1B

$\begin{matrix} A.A^{–1} \end{matrix}$B A = A^–1BⁿA