# Involutory matrix

## From Wikipedia, the free encyclopedia

In mathematics, an **involutory matrix** is a square matrix that is its own inverse. That is, multiplication by the matrix **A** is an involution if and only if **A**^{2} = **I**, where **I** is the *n* × *n* identity matrix. Involutory matrices are all square roots of the identity matrix. This is simply a consequence of the fact that any nonsingular matrix multiplied by its inverse is the identity.[1]