1. A square matrix A, of order 3, has |A|=5, find |A adj. A|.

let A be a square matrix of order n.
$A\left(adjA\right)=\left|A\right|I_n$ , where $I_n be the identity matrix of order n.$
therefore
$$\begin{gathered} \left|A\left(adjA\right)\right|=\left|\left|A\right|I_n\right| \\ ={\left|A\right|}^n\left|I_n\right| \\ ={\left|A\right|}^n \left[\right|I_n| =1] \end{gathered}$$
given |A| = 5 and n = 3
therefore
$$\begin{gathered} \left|A\left(adjA\right)\right|=5^3 \\ =125 \end{gathered}$$
hope this helps you.