Question

If A is a non-singular square matrix such that |A| = 10, find |A⁻¹|.

Answer 1

For any non-singular matrix A,
$$\begin{gathered} \left|A^{-1}\right|=\frac{1}{\left|A\right|} \\ \therefore \left|A^{-1}\right|=\frac{1}{10}\left[\because \left|A\right|=10\right] \end{gathered}$$