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Abstract Algebra

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Properties of Commutators

ABSALG-1EHKLG

Let $x,y\in\mathbb{C}$. Define the commutator as the operation $[x,y]=xy-yx$.

Which of the following best describes this operation on $\mathbb{C}$?

A

Associative, commutative

B

Not associative, commutative

C

Associative, not commutative

D

Not associative, not commutative