Question

A and B are square matrices and A is non-singular matrix, $(A^{-1}BA{)}^n,nϵI^{+}$ is equal to

• A. $A^{-n}{B}^n{A}^n$
• B. $A^n{B}^n{A}^{-n}$
• C. $A^{-1}{B}^{n}A$
• D. $A^{-1}B{A}^n$

Answer 1

The correct option is C $A^{-1}{B}^{n}A$

For n = 2 $\Rightarrow \left(A^{-1}\right)\left(A^{-1}BA\right)=A^{-1}{B}^{2}A\left(A^{-1}{B}^{3}A\right)$ and soon
Thus $(A^{-1}BA{)}^n=A^{-1}{B}^{n}A$