Is matrix multiplication for square matrices commutative, associative, or distributive?
only associative and distributive
Matrix multiplication for square matrices is associative but not commutative or distributive.
Associativity means that for three square matrices A, B, and C, (AB)C = A(BC). This allows us to change the grouping of the matrices when we multiply them together without changing the result.
However, matrix multiplication for square matrices is not commutative, which means that AB ≠ BA. The order in which the matrices are multiplied affects the result.
Similarly, matrix multiplication for square matrices is not distributive, which means that (A + B)C ≠ AC + BC or A(C + D) ≠ AC + AD. In other words, the distributive property of multiplication does not hold for matrix multiplication.
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