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:

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

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

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