Question:
If $A=\left[a_{i j}\right]$ is a $3 \times 3$ scalar matrix such that $a_{11}=2$, then write the value of $|A|$.
Solution:
A scalar matrix is a diagonal matrix, in which all the diagonal elements are equal to a given scalar number.
Given: $\mathrm{A}=\left[a_{i j}\right]$ is $3 \times 3$ matrix, where $a_{11}=2$
$\Rightarrow \mathrm{A}=\left[\begin{array}{lll}2 & 0 & 0\end{array}\right.$
$\begin{array}{lll}0 & 2 & 0\end{array}$
$\left.\begin{array}{lll}0 & 0 & 2\end{array}\right]$
$\Rightarrow|\mathrm{A}|=\mid \begin{array}{lll}2 & 0 & 0\end{array}$
$\begin{array}{lll}0 & 2 & 0\end{array}$
$\begin{array}{lll}0 & 0 & 2\end{array}$
$=2 \times \mid 20$
$\begin{array}{ll}0 & 2\end{array}$
[Expanding along $\mathrm{C}_{1}$ ]
$=2 \times 2 \times 2=8$