Question

If A is a square matrix such that |A| = 2, write the value of |A A^T|.

Answer 1

\[\text{ In a square matrix, }\left| A \right| = \left| A^T \right| . \] 
\[\text{ Since they are of same order, }\left| A A^T \right| = \left| A \right|\left| A^T \right| . \] 
\[\text{ Given: }\left| A \right| = 2\] 
\[ \Rightarrow \left| A A^T \right| = 2 \times 2 = 4\]