Question

If $A$ and $B$ are matrices and $B=AB{A}^{-1}$ then the value of $(A+B)(A-B)$ is

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

Answer 1

Answer: (B)

$B=AB{A}^{-1}($ Given $)$
But $B=BA{A}^{-1}$
$\therefore AB{A}^{-1}=BA{A}^{-1}$
$\Rightarrow AB=BA$
Now $(A+B)(A-B)$
$=A^2-AB+BA-B^2$
$=A^2-AB+AB-B^2$
$[\because AB=BA]$
$=A^2-B^2$
$\therefore (A+B)(A-B)=A^2-B^2$