If \(A\) is an inversible, then \(A^{-1}\) is also inversible and
$$(A^{-1})^{-1}=A$$
Proof
Suppose that a matrix \(A\) is invertible. Then there exists \(A^{-1}\) such that
$$AA^{-1}=A^{-1}A=I$$
where \(I\) is an identity matrix.
By this equation, we can also consider that \(A\) is the inverse matrix of \(A^{-1}\).
Since the uniqueness of inverse matrix, we can conclude that
$$(A^{-1})^{-1}=A$$