Question

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

Answer 1

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