Is matrix multiplication for square matrices commutative, associative, or distributive?
only associative and distributive
Matrix multiplication is associative, but it is not commutative or distributive for square matrices.
Associativity: This means that for three square matrices of the same size A, B, and C, the following holds true: (AB)C = A(BC).
Commutativity: This means that for two square matrices A and B, the following does not hold true, in most cases: AB = BA. In other words, the order in which two square matrices are multiplied matters.
Distributivity: This means that for three square matrices A, B, and C, the following does not hold true, in most cases: A(B+C) = AB + AC or (B+C)A = BA + CA.
It is important to note that while matrix multiplication is not commutative or distributive in general, there are some special cases where it may be. For example, the identity matrix commutes with any square matrix, and the distributive law holds true if one of the matrices is a scalar.
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