Identity matrix

Description

Let $R$ be a ring and let $n \ge 0$ be an integer. The identity matrix $I_n$ is the $n \times n$ matrix over $R$ with entries $1$ on the main diagonal and $0$ elsewhere. Its entries are $(I_n)_{ij} = \delta_{ij}$, where $\delta_{ij} = 1$ if $i = j$ and $\delta_{ij} = 0$ otherwise. For each $m \times n$ matrix $A$, $A I_n = A$ and $I_m A = A$.