Let $A \in L(H)$, for a Hilbert space $H$. If $A$ is invertible, why is $A^*A$ invertible, too?
2026-04-24 03:47:50.1777002470
If $A$ is invertible, so is $A^*A$
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If $AB=BA=1$ then $A^*B^*=B^*A^*=1$ and hence $A^*ABB^*=BB^*A^*A=1$