Let A = [a hi ], B = [b ij ], and C = [C jk ]
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Let A = [ahi], B = [bij], and C = [Cjk] 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.
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Related Book For 
Differential Equations And Linear Algebra
ISBN: 9780134497181
4th Edition
Authors: C. Edwards, David Penney, David Calvis
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