I know it's basics, but I am really confused:
If $A^*$ is the adjoint of $A$ and $AA^*=I$, where $I$ is an identity matrix, can we conclude that $A^*=A^{-1}$?
If not, why not?
2026-03-25 05:05:31.1774415131
Invertible matrices and Adjoints
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Yes, inverse is unique, if a square matrix $A$ and $B$ satisfy $$AB=I$$, then $B=A^{-1}$.
Hence $A^*=A^{-1}$