I don't know if I'm missing something out but is this just not proved by saying ${\rm Im} (AB)$ subspace of ${\rm Im}(A)$ so ${\rm rank}(AB) \leq {\rm rank}(A)$?
2026-04-02 21:40:49.1775166049
Given $n \times n$ matrices, $A$ and $B$, show that ${\rm rank}(AB) \leq {\rm rank}(A)$
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