1_0_2_−131][31_21_10_]=[51_42].{\displaystyle {\begin{aligned}{\begin{bmatrix}{\underline {1}}&{\underline {0}}&{\underline {2}}\\-1&3&1\\\end{bmatrix}}{\begin{bmatrix}3&{\underline {1}}\\2&{\underline {1}}\\1&{\underline {0}}\\\end{bmatrix}}&={\begin{bmatrix}5&{\underline {1}}\\4&2\\\end{bmatrix}}.\end{aligned}}}Matrix multiplication satisfies the rules (AB)C = A(BC) (associativity), and (A+B)C = AC+BC as well as C(A+B) = CA+CB (left and right distributivity), whenever the size of the matrices is such that the various products are defined.[6] The product AB may be defined without BA being defined, namely if A and B are m-by-n and n-by-k matrices, respectively, and m ≠ k. Even if both products are defined, they need not be equal, i.e., generally one hasAB ≠ BA,i.e., matrix multiplication is not commutative, in marked contrast to (rational, real, or complex