Question

If A, B and C are 3 invertible matrices and BAC = I, what is the value of A.

• 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
Premultiplying equation with $B^{-1}$
$B^{-1}BAC=B^{-1}$
$i.e.,AC=B^{-1}$
Post multiplying equation by $C^{-1}$
$AC{C}^{-1}=B^{-1}{C}^{-1}$
$A=B^{-1}{C}^{-1}$