# Definition of Identity Matrix

A square matrix in which all the main diagonal elements are 1’s and all the remaining elements are 0’s is called an Identity Matrix. Identity Matrix is also called **Unit Matrix** or **Elementary Matrix**. Identity Matrix is denoted with the letter “**I**_{n×n}”, where *n×n* represents the order of the matrix. One of the important properties of identity matrix is: *A*×*I*_{n×n} = *A*, where *A* is any square matrix of order *n×n*.

**Examples of Identity Matrix**

are identity matrices of order 1×1, 2×2, 3×3,………… n×n.

**Example 1: **Give an example of 4×4 order identity or unit matrix.

**Solution: **

We know that the identity matrix or unit matrix is the one with all ‘ones’ on the main diagonal and other entries as ‘zeros’. So the 4×4 order identity or unit matrix can be written as follows:

**Example 2: **Is the following matrix an Identity matrix?

**Solution: **

No, the given matrix is not an identity matrix, because unit or identity matrix is a square matrix. In this case *A* is a matrix of order 3×4, which is not a square matrix.

**Example 3: **Is the following matrix a Unit matrix?

__Solution:__** **

No, the given matrix is not a unit matrix, since a unit matrix must only contain the value of 0 beside the diagonal values of 1.

**Example 4: **What is the multiplication of a matrix *A*^{ }by the identity matrix of order 5, given that *A*^{ }is a square matrix of order 5?

__Solution__**: **

We know that identity matrix is the one which satisfies *A*×*I*_{n×n} = *A*, where *A* is any square matrix of order *n×n*. Therefore the multiplication of a 5*×*5 matrix *A *by the identity matrix of order 5 is the same as *A*.