Question

If A is an invertible matrix such that |A⁻¹| = 2, find the value of |A|.

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{know}, \\ {\left|A\right|}^{-1}=\frac{1}{\left|A\right|} \\ \Rightarrow 2=\frac{1}{\left|A\right|}\left[\because {\left|A\right|}^{-1}=2\right] \\ \Rightarrow \left|A\right|=\frac{1}{2} \end{gathered}$$