Show that (a) AB AC A(B C) and (b) BA CA (B C)A In general, if A is an m Atilde n matrix and B, C are n Atilde p matrices, then AB AC A(B C) For n Atilde p matrices B, C and a p Atilde q matrix A, it follows that BA CA (B C)A These two results are called the Distributive Laws for Matrix Multiplication over Matrix Addition Let L 3 5 , and C 0 3 2 2 7 6

Question: Show that (a) AB + AC = A(B + C); and (b) BA + CA = (B + C)A. [In general, if A is an

Show that
(a) AB + AC = A(B + C); and
(b) BA + CA = (B + C)A.
[In general, if A is an m Ã— n matrix and B, C are n Ã— p matrices, then AB + AC = A(B + C). For n Ã— p matrices B, C and a p Ã— q matrix A, it follows that BA + CA = (B + C)A. These two results are called the Distributive Laws for Matrix Multiplication over Matrix Addition.]
Let

L 3 5 , and C=[ 0 3-2 -2 7 6

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