Let A and B me matrices such that the product AB is defined. One has to proove that r(AB) <= r(A) and r(AB) <= r(B).(adsbygoogle = window.adsbygoogle || []).push({});

My first thoughts are: let A be 'mxn' and B be 'nxp', so AB is 'mxp'. Further on, we know that r(A) <= min{m, n}, r(B) <= min{n, p} and r(AB) <= min{m, p}. I'm stuck here, although I tried to work something out with the inequalities, but without success. Any hints would be appreciated.

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# Another matrix rank proof

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