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