**Unit Matrix** or **Identity Matrix** is a square matrix whose all diagonal elements is 1 and all off-diagonal elements are zero. It is usually denoted by the capital letter ‘**I**‘.

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A square matrix P = [x_{ij}] is said to be unit matrix or identity matrix if x_{ij} = 1 when i = j and x_{ij} = 0 when i ≠ j.

## Identity matrix examples

The example of an identity matrix of order 3 (or matrix size is 3 x 3) is given below.

\[I=\begin{bmatrix} 1 &0 &0 \\ 0& 1 &0 \\ 0&0 & 1 \end{bmatrix}\]

The example of an identity matrix of order 2 (or matrix size is 2 x 2) is given below.

\[I=\begin{bmatrix} 1 &0 \\ 0& 1 \end{bmatrix}\]

## Identity matrix properties

Let P be a matrix.

1. PI = IP = P

2. The self multiplication of the identity matrix ‘**n’** times gives identity matrix i.e. I^{n} = I.

3. The inverse of the identity matrix is the identity matrix itself i.e. I^{-1} = I.

4. The determinant of an identity matrix is 1 i.e. |I| = 1.

5. An unit matrix or identity matrix is a scalar matrix.