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...Some viewpoints on matrix multiplication ab ef let a and b then cd gh ae bg af bh cdgh ce dg cf dh there are many ways to interpret this remarkable operation perhaps the most natural one being interpretation of as function composition linear functions from which associativity follows directly but following formulas suggest other interpretations e c g d f h i right by corresponds column operations left row we can express sum matrices each rank in algebra you choose wish use at given point an argument what same calculations for abc qrs defandb tuv ghi xyz aq bt cx ar bu cy bv cz def dq et fx dr eu fy ds ev fz gq ht ix gr hu iy gs hv iz qd te xf rd ue yf sd ve zf...