Identity matrix

A square matrix $I$ with entries $1$ on the main diagonal and $0$ otherwise: $$ I_{ij} = \delta_{ij} $$ where $\delta$ is the Kronecker symbol.

If $R$ is a ring with identity and 0 and 1 are interpreted as elements of $R$, then $I$ is the identity element in the matrix ring $M_n(R)$.