An **identity matrix**, notated $I_n$, is an $n\times n$ [[diagonal matrix]] with its diagonal entries all equal to one $ I_{n}=\left(\begin{array}{cccc}1 & 0 & \cdots & 0 \\ 0 & 1 & \cdots & 0 \\ \vdots & \vdots & \ddots& \vdots \\ 0 & 0 & \cdots & 1\end{array}\right) $