Question

If A is a square matrix such that A (adj A) = 10I, then $\left|A\right|$ = ____________________.

Answer 1

Given:
A is a square matrix
A(adj A) = 10I


As we know,
$$\begin{gathered} A\left(\mathrm{adj}A\right)=\left|A\right|I \\ \Rightarrow 10I=\left|A\right|I \\ \Rightarrow \left|A\right|=10 \end{gathered}$$


Hence, $\left|A\right|=\underline{10}$.