Given a matrix $A$, if the rank of $A$ is defined to be the highest order of non-vanishing minor of $A$.
If we apply the above definition, how to check that $\operatorname{rank}(AB) \leq \operatorname{rank}(A)$?
Given a matrix $A$, if the rank of $A$ is defined to be the highest order of non-vanishing minor of $A$.
If we apply the above definition, how to check that $\operatorname{rank}(AB) \leq \operatorname{rank}(A)$?
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