Question

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

Answer 1

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