Properties of Matrix Multiplication
If \(A\text{,}\) \(B\text{,}\) and \(C\) are matrices such that the following operations are defined, it follows that
 Associativity:
\(A(BC) = (AB)C\text{.}\)
 Distributivity:

\(A(B+C) = AB+AC\text{.}\)
\((A+B)C = AC+BC\text{.}\)