Prove that the distributive property holds for matrix addition and matrix multiplication. In other words, suppose $A,B,C,D,E,F$ are matrices whose sizes are such that $A(B+C)$ and $(D+E)F$ make sense. Prove that $AB+AC$ and $DF+EF$ both make sense and that $A(B+C) = AB + AC$ and $(D + E)F = DF + EF$.

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