Question

If $A$ is a square matrix, then $A\left(adjA\right)$ equals

• A. $\left|A\right|$
• B. $I$
• C. $\left|A\right|I$
• D. $0$

Answer 1

The correct option is C $\left|A\right|I$

$A^{-1}=\frac{adjA}{|A|}$

multiplying both sides with $A$ gives

$A{A}^{-1}=\frac{A\left(adjA\right)}{|A|}$

$\therefore A\left(adjA\right)=|A|I$

Hence, option C.