Let $A$ be a square matrix of order 3, write the value of $|2 A|$, where $|A|=4$.

Solution:

Theorem: If $A$ be $k \times k$ matrix then $|p A|=p^{k}|A|$.
Given: $p=2, k=3$ and $|A|=4$
$\begin{array}{l}
|2 A|=2^{3} \times|A| \\
=8 \times 4 \\
=32
\end{array}$