Identity Matrix

Identity Matrix

## Definition / Concept

A square diagonal matrix whose diagonal elements are all $1$ is called an identity matrix.

$$I_n=\begin{bmatrix}1&0&\cdots&0\\0&1&\cdots&0\\\vdots&\vdots&\ddots&\vdots\\0&0&\cdots&1\end{bmatrix}$$

## Formula

$$AI_n=I_nA=A$$

whenever the matrix dimensions are compatible.

## Usage

- Acts as the multiplicative identity in matrix multiplication.