Let A a hi , B b ij , and C C jk be matrices of sizes m x n, n x p, and p x q, respectively To establish the associative law A(BC) (AB)C, proceed as follows By Equation (16) the hjth element of AB is By another application of Equation (16), the hkth element of (AB)C is Show similarly that the double sum on the right is also equal to the hkth element of A(BC) Hence the m q matrices (AB)C and A(BC) are equal 11 i l 1 ahibij

Question: Let A = [a hi ], B = [b ij ], and C = [C jk ] be matrices of sizes m x n, n

Let A = [a_hi], B = [b_ij], and C = [C_jk] be matrices of sizes m x n, n x p, and p x q, respectively. To establish the associative law A(BC) = (AB)C, proceed as follows. By Equation (16) the hjth element of AB is

11 i=l 1 ahibij.

By another application of Equation (16), the hkth element of (AB)C is

Show similarly that the double sum on the right is also equal to the hkth element of A(BC). Hence the m × q matrices (AB)C and A(BC) are equal.

11 i=l 1 ahibij.

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