Question

If for any $2\times 2$ square matrix $\text{A, A (adj A)}=\left[\begin{array}{cc}8& 0\\ 0& 8\end{array}\right]$, then find the value of $|A|$.

Answer 1

$\text{Given,}$
$\text{A (adj. A) =}\left[\begin{array}{cc}8& 0\\ 0& 8\end{array}\right]$
$\text{by using property}$
$\text{If A is a square matrix of order n, then}$
$\text{A (adj A) = |A|}{I}_n$
$\therefore |A|I_2=\left[\begin{array}{cc}8& 0\\ 0& 8\end{array}\right]\Rightarrow |A|=\left|\begin{array}{cc}8& 0\\ 0& 8\end{array}\right|=64$