Commutative property holds if MN=NM, for matrices M and NMatrix multiplication isn’t possible for matrices that aren’t square e.g if we have2 matrices M and NMij⋅Njk=Njk⋅MijAs seen in the right hand side of the expression above the matrix isn’t even possibleHence matrix multiplication is not possibleAlso matrix multiplication is not generally possibly for square matrices, to this endwe give a counter-exampleLet A=(6235) and B=(−3125)A.B=(−15−12729)B.A=(−1416126)Therefore, since A⋅B=B⋅A, hence matrix multiplication isn’t commutative
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