Question

If A be a square matrix such that $\left|adjA\right|={\left|A\right|}^2$, then the order of A is __________________.

Answer 1

Given:
A is a square matrix
$\left|\mathrm{adj}A\right|={\left|A\right|}^2$


As we know,
$$\begin{gathered} \left|\mathrm{adj}A\right|={\left|A\right|}^{n-1},\mathrm{where}n\mathrm{is}\mathrm{the}\mathrm{order}\mathrm{of}A \\ \Rightarrow {\left|A\right|}^2={\left|A\right|}^{n-1} \\ \Rightarrow 2=n-1 \\ \Rightarrow n=3 \end{gathered}$$


Hence, the order of A is 3.