The **identity matrix** (denoted $\mathbf I$, $\mathbb I$, $\mathbb 1$ or just $I$) is the $n\times n$ matrix containing $1$’s along its diagonal. For example, with $n = 3$:

$$ \mathbf I_3 = \begin{pmatrix} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1\end{pmatrix}$$