Question:
If $A=\left[a_{i j}\right]$ is a $3 \times 3$ diagonal matrix such that $a_{11}=1, a_{22}=2 a_{33}=3$, then find $|A| .$
Solution:
If $A=\left[\mathrm{a}_{\mathrm{ij}}\right]$ is a diagonal matrix of order $\mathrm{n}$, then $|A|=\mathrm{a}_{11} \times \mathrm{a}_{22} \times \mathrm{a}_{33} \times \ldots \times \mathrm{a}_{\mathrm{nn}}$.
Given : $a_{11}=1, \mathrm{a}_{22}=2$ and $\mathrm{a}_{33}=3$
$\Rightarrow|A|=1 \times 2 \times 3=6 \quad$ [Applying the above property]