# If $A$ is invertible, so is $A^*A$

Let $A \in L(H)$, for a Hilbert space $H$. If $A$ is invertible, why is $A^*A$ invertible, too?

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## 1 Answer

If $AB=BA=1$ then $A^*B^*=B^*A^*=1$ and hence $A^*ABB^*=BB^*A^*A=1$

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