Inverse and a power
Task number: 2429
Let \(\mathbf B\) be the inverse of \(\mathbf A^2\). Prove that \(\mathbf A\) is regular and determine its inverse.
Resolution
From \(\mathbf A^2\mathbf B = \mathbf A\mathbf A\mathbf B = \mathbf I_n\) we get that \(\mathbf A^{-1}=\mathbf A\mathbf B\).
