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# Is matrix multiplication commutative or associative?

**Matrix multiplication is associative.** The associative law states that the way numbers are grouped does not matter and that the sum or product obtained will be the same.

The commutative law of multiplication does not apply to matrices. The commutative law states that the order of numbers can be changed without changing the answer. A matrix is an array of numbers. Matrix multiplication is done using the "dot product" method. After obtaining the products of matching members in each row and column, they are all summed up. Since matrix multiplication is not commutative, if the order of multiplication is changed, the answer is different.

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