Understanding the Non-Commutativity, Associativity, and Non-Distributivity of Matrix Multiplication

Is matrix multiplication for square matrices commutative, associative, or distributive?

Matrix multiplication is not commutative

Matrix multiplication is not commutative. This means that for two square matrices A and B, in general, AB is not equal to BA. In other words, the order in which the matrices are multiplied matters.

Matrix multiplication is associative. This means that for three square matrices A, B, and C, (AB)C is equal to A(BC). In other words, it does not matter how we group the matrices, the result will be the same.

Matrix multiplication does not follow the distributive property. This means that for square matrices A, B, and C, A(B + C) is not equal to AB + AC. In other words, matrix multiplication does not distribute over addition.

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