Involutory matrix

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