Prove Theorem 2(b) and 2(c). Use the row-column rule. The (i,j)-entry in A(B+C) can be written as 71 0;1(b1; + cij) + ... + ain(bnj + Cn)) or aix(bx; + ck)) k=1 2. Let A be an mxn matrix, and let B and C have sizes for which the indicated sums and products are defined. a. A(BC) = (AB)C (associative law of multiplication) b. A(B+C) = AB + AC (left distributive law)