Let V be the set of all n x n matrices of real numbers. Define an operation of "addition" by ABB = (AB + BA) for all A, B EV. Define an operation of "scalar multiplication" by a A = 0 for all a ER and A € V. Under the operations and the set V is not a vector space. The vector space axioms (see 5.1.1 (1)-(10)) which fail to hold are and "

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