Let $A,U \in {M_n}$ and $U$ is unitary matrix.Is this true that $Rank(AU)=Rank(A)$?
2026-04-01 07:14:54.1775027694
Simple question in Rank
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If $U$ is a unitary matrix, then it is invertible.
If $B$ is any invertible matrix, then image$(AB)$=image$(A)$ because image$(B)=\mathbb C^n$.
In particular, rank$(AB)$=rank$(A)$.