# Identity or Unit Matrix – Definition and Examples

Here you will learn what is the identity or unit matrix definition with examples.

Let’s begin –

## Identity or Unit Matrix

Definition : A square matrix A = $$[a_{ij}]_{n\times n}$$ is called a identity or unit matrix if

(i) $$a_{ij}$$ = 0 for all i $$\ne$$ j and,

(ii) $$a_{ii}$$ = 1, for all i

In other words, a diagonal matrix in which all the diagonal elements is unity is called the unit matrix.

The identity matrix of order n is denoted by $$I_n$$.

## Examples :

1). $$\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$$ is a identity matrix.

The order of above matrix is $$3 \times 3$$ and it is denoted by $$I_3$$.

2). $$\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$$ is a identity matrix.

The order of above matrix is $$2 \times 2$$ and it is denoted by $$I_2$$.

3). $$\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}$$ is a identity matrix.

The order of above matrix is $$4 \times 4$$ and it is denoted by $$I_4$$.