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.
Associative: Matrix multiplication is associative, which means the order in which the matrices are multiplied does not matter. That is, for any three square matrices A, B, and C of compatible sizes, (A*B)*C = A*(B*C).
Commutative: Matrix multiplication is not commutative, which means the order in which the matrices are multiplied matters. In other words, for two square matrices A and B of compatible sizes, A*B is not necessarily equal to B*A.
Distributive: Matrix multiplication is also not distributive, which means that the product of a sum of matrices is not equal to the sum of the products of each matrix. That is, for any three square matrices A, B, and C of compatible sizes, A*(B+C) is not necessarily equal to A*B + A*C. However, scalar multiplication can be distributed over matrix multiplication.
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