Identity Matrix

We define the identity matrix \( I \) as a matrix with \( 1 \) across all its diagonals. For example the 2D identity matrix is

\begin{align*} \begin{pmatrix}

1 & 0 \\\\
0 & 1

\end{pmatrix} \end{align*}

Multiplying any matrix by this matrix is the same as not multiplying by it at all.