Question:
If $I_{3}$ denotes identity matrix of order $3 \times 3$, write the value of its determinant.
Solution:
In an identity matrix, all the diagonal elements are 1 and rest of the elements are 0.
Here,
$I_{3}=\mid \begin{array}{lll}1 & 0 & 0\end{array}$
$\begin{array}{lll}0 & 1 & 0\end{array}$
$\begin{array}{lll}0 & 0 & 1\end{array}$
$=1 \times \mid \begin{array}{ll}1 & 0\end{array}$
$\begin{array}{ll}0 & 1\end{array} \quad\left[\right.$ Expanding along $\left.\mathrm{C}_{1}\right]$
$=1$
$\Rightarrow \mathrm{I}_{3}=1$