Question:
If $A=\operatorname{diag}(2,3,4)$, then $\left|A^{2}\right|=$
Solution:
Given: $A=\operatorname{diag}(2,3,4)$
$\left|A^{2}\right|=|A|^{2} \quad\left(\because\left|A^{n}\right|=|A|^{n}\right)$
$=(2 \times 3 \times 4)^{2}$
$=(24)^{2}$
$=576$
Hence, $\left|A^{2}\right|=\underline{576}$.