Identity Matrix, Unit Matrix
Definition
A diagonal matrix of size $n\times n$ with all diagonal elements being $1$ is called an identity matrix or unit matrix, denoted as $I_{n}$ or $I_{n\times n}$.
$$ I_{n\times n}= \begin{bmatrix} 1 & 0 & \cdots & 0 \\ 0 & 1 & \cdots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \cdots & 1 \end{bmatrix} $$
Description
The identity matrix is the identity element for matrix multiplication. This means that for any $n\times n$ matrix $A$, the following equation holds:
$$ I_{n}A=A=AI_{n} $$
Properties
Determinant
Since the identity matrix is a diagonal matrix, its determinant is $1$.
$$ \det I = 1 $$