Let A and B be m×n matrices, with A=[aij] and B=[bij]. The operation of addition is defined by taking the sum A + B to be the m×n matrix C, where C=[cij] and cij = aij + bij. The sum A + B is not defined if A and B are not of the same order. This operation + of addition on the set of all m×n matrices is associative and commutative.