Question

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

Answer 1

We know that, by property of adjoint and inverse of matrix
$A\left(adjA\right)=|A|I\cdots \left(i\right)$
$\therefore \left[\begin{array}{cc}10& 0\\ 0& 10\end{array}\right]=10\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$
Comparing with equation $\left(i\right)$, we get
$|A|=10$