Question

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

Answer 1

As, $\text{A(adj.A)=|A| I}$=$\left[\begin{array}{cc}8& 0\\ 0& 8\end{array}\right]=8\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$=$\text{8 I}$
On comparing, we get : $\text{|A|=8}$