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Question
If A is an invertible matrix such that |A−1| = 2, find the value of |A|.
Solution
We know,
\[ \left| A \right|^{- 1} = \frac{1}{\left| A \right|}\]
\[ \Rightarrow 2 = \frac{1}{\left| A \right|} \left[ \because \left| A \right|^{- 1} = 2 \right]\]
\[ \Rightarrow \left| A \right| = \frac{1}{2}\]
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