$\begin{align}  & \text{A unit matrix of order }3\times 3\text{ is represented }I=\left( \begin{matrix}   1 & 0 & 0  \\   0 & 1 & 0  \\   0 & 0 & 1  \\\end{matrix} \right) \\ & \text{So the determinant is will be} \\ & \left| I \right|=\left| \begin{matrix}   1 & 0 & 0  \\   0 & 1 & 0  \\   0 & 0 & 1  \\\end{matrix} \right| \\ & \text{By mere looking at this }\left| I \right|=1 \\ & \text{But for the sake of proper understanding of the solution} \\ & \text{I will show the working} \\ & \left| I \right|=1\left| \begin{matrix}   1 & 0  \\   0 & 0  \\\end{matrix} \right|-0\left| \begin{matrix}   0 & 0  \\   0 & 1  \\\end{matrix} \right|+0\left| \begin{matrix}   0 & 1  \\   0 & 0  \\\end{matrix} \right| \\ & \left| I \right|=1(1-0)-0(0-0)+0(0-0) \\ & \left| I \right|=1-0+0=1 \\\end{align}$