Matrix - Identity Matrix

The identity matrix is the identity element for matrix multiplication.

The identity matrix is a square matrix ($\text{n}\times n$) with zeros in all positions except for the main diagonal, where there are ones.

A $n\times n$ identity matrix is denoted with $I_n$:

$$I_n=\left[\begin{array}{ccccc}1& 0& 0& \cdots & 0\\ 0& 1& 0& \cdots & 0\\ 0& 0& 1& \cdots & 0\\ ⋮& ⋮& ⋮& \ddots & ⋮\\ 0& 0& 0& \cdots & 1\end{array}\right]$$

Example for $n=3$:

$$I_3=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$$