Question

For any $2\times 2$ matrix, if $A\left(adjA\right)=\left[\begin{array}{cc}10& 0\\ 0& 10\end{array}\right]$, then
$\left|A\right|$ is equal to

• A. $20$
• B. $100$
• C. $10$
• D. $0$

Answer 1

The correct option is C $10$

$A\left(adjA\right)=\left[\begin{array}{cc}10& 0\\ 0& 10\end{array}\right]$
We know $A\left(adjA\right)=|A|I_2$
$\therefore |A|I_2=\left[\begin{array}{cc}10& 0\\ 0& 10\end{array}\right]$
$\Rightarrow |A|I_2=10I_2$
$\Rightarrow |A|=10$