SOLUTION: Multiplication of matrices are only commutative for some cases of matrices. What are these cases?

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Off the top of my head I can only think of these cases where commutativity holds:


where I is the identity matrix


where is the inverse of matrix A


Also, according to Wolfram Mathworld, "...matrix multiplication is not, in general, commutative (although it is commutative if A and B are diagonal and of the same dimension)."



For instance, if you have matrices diagonal matrices A and B


,


the first product AB is




and the second product BA is



which is the same product as AB. So if you were to do this with general entries of the matrices A and B, you would find that only if A and B are diagonal matrices and they are both the same size