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 \(\mathbf A^{-1}=\mathbf A\mathbf B\).

Difficulty level: Easy task (using definitions and simple reasoning)
Proving or derivation task
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