Question:
If $A$ is a square matrix such that $|A|=2$, write the value of $\left|A A^{\top}\right|$.
Solution:
In a square matrix, $|\mathrm{A}|=\left|\mathrm{A}^{\mathrm{T}}\right|$.
Since they are of same order, $\left|\mathrm{A} \mathrm{A}^{\mathrm{T}}\right|=|\mathrm{A}|\left|\mathrm{A}^{\mathrm{T}}\right|$.
Given : $|\mathbf{A}|=2$
$\Rightarrow\left|\mathrm{A} \mathrm{A}^{\mathrm{T}}\right|=2 \times 2=4$
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