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radou

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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.