An **involutory matrix** is a square matrix which when multiplied by itself, gives the resultant matrix as identity matrix. In other words, matrix **B** is called involutory if B^{2} = I. Here I is the identity matrix having size same as of matrix B.

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## Involutory matrix Examples

The examples of 2 x 2 involutory matrices are

1.

2.

The examples of 3 x 3 involutory matrices are

1.

2.

## How to check whether a matrix is involutory matrix or not?

We can easily check whether a matrix is involutory or not. For this, check the square of a matrix is the identity matrix or not i.e. B^{2} = I, where B is a matrix and I is the identity matrix. If this condition is satisfied then the matrix is involutory. If the condition is not satisfied then the matrix is not involutory.