If A = diag (2, 3, 4)
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, $\left|A^{2}\right|=\underline{576}$.

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