Show that
(a) AB + AC = A(B + C); and
(b) BA + CA = (B + C)A.
[In general, if A is an m × n matrix and B, C are n × p matrices, then AB + AC = A(B + C). For n × p matrices B, C and a p × 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

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