Definition:Unit Matrix

Definition
Let $R$ be a ring with unity whose zero is $0_R$ and whose unity is $1_R$.

Let $\mathcal M_R \left({n}\right)$ be the $n \times n$ matrix space over $R$.

Then the identity matrix (of order $n$) of the ring $\left({\mathcal M_R \left({n}\right), +, \times}\right)$ is defined as:


 * $\mathbf I_n := \left[{a}\right]_{n}: a_{i j} = \delta_{i j}$

where $\delta_{i j}$ is the Kronecker delta.

That is, it is the square matrix where every element on the diagonal is equal to $1_R$, and $0_R$ elsewhere.

Also see

 * Identity Matrix is Unity of Ring of Square Matrices, where $\mathbf I_n$ is shown to be the unity of $\mathcal M_R \left({n}\right)$.