Question

If $A,B$ and $C$ are invertible matrices and $BAC=I,$ the value of $A$ is

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

Answer 1

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

Given that,
$BAC=I$
Pre-multiplying the given equation with $B^{-1}$
$B^{-1}BAC=B^{-1}$
$i.e.,AC=B^{-1}$
Post multiplying the above equation by $C^{-1}$
$AC{C}^{-1}=B^{-1}{C}^{-1}$
$A=B^{-1}{C}^{-1}$