# Involutory matrices An _involutory matrix,_ is an [$n\times n$ matrix](Matrices.md#^34a807), $A$, that's its own [inverse](Operator%20inverse.md#Matrix%20inverse) ($A^{-1}=A$). This therefore also means that $A^2 = A^{-1}A=\mathbb{1},$ where $\mathbb{1}$ is the $n\times n$ identity matrix. #MathematicalFoundations/Algebra/AbstractAlgebra/LinearAlgebra/Operators #MathematicalFoundations/Algebra/AbstractAlgebra/LinearAlgebra/Operators/Matrices #MathematicalFoundations/Analysis/FunctionalAnalysis