Question

If $A,B,C$ are square matrices of same order such that $AB=BA,C^2=B,$ then $(A^{-1}CA{)}^2$ is equal to

• A. $B^2$
• B. $A^2$
• C. $C^2$
• D. $C$

Answer 1

The correct option is C

$C^2$

Given, $AB=BA,C^2=B$

$\Rightarrow (A^{-1}CA{)}^2=(A^{-1}CA\left)\right(A^{-1}CA)=A^{-1}CICA=A^{-1}{C}^{2}A$

$=A^{-1}BA=A^{-1}\left(AB\right)=IB=B=C^2$