Question

If $A$ and $B$ are square matrices of the same order such that $(A + B) (A -B) = A^2-B^2$ then $(ABA^{-1} )^2=$

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

Answer 1

Answer: (B)

$B^2$

Answer 2

Given, $(A+B)(A-B)=A^{2}-B^{2}$
$\Rightarrow A^{2}-A B+B A-B^{2}=A^{2}-B^{2}$
$\Rightarrow A B=B A$
Now, $\left(A B A^{-1}\right)^{2}=\left(B A A^{-1}\right)^{2}=B^{2}$