Question

If A is a square matrix of order 3 such that |adj A| = 64, find |A|.

Answer 1

For any square matrix of order n, \[\left| adj A \right| = \left| A \right|^{n - 1} \]
\[ \Rightarrow 64 = \left| A \right|^2 \left[ \because \left| adj A \right| = 64 \right]\]
\[ \Rightarrow \left| A \right| = \pm 8\]