A question on Involuntary matrices If A is a square matrix such that $A^2= I, then A^{-1} $is equal to what? (where I is the identity matrix)

Suppose $B$ is the inverse of $A$, then $AB=BA=I$.

Now $AAB=A\implies A^2B=A\implies IB=A\implies B=A.$ that is $A$ is it's own inverse.