## Inverse and a power

Let $$\mathbf B$$ be the inverse of $$\mathbf A^2$$. Prove that $$\mathbf A$$ is regular and determine its inverse.
From $$\mathbf A^2\mathbf B = \mathbf A\mathbf A\mathbf B = \mathbf I_n$$ we get that $$\mathbf A^{-1}=\mathbf A\mathbf B$$.