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Abstract Algebra

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Moderate

Associativity and Commutivity of Matrix Groups

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Consider the set $\textrm{Mat}_{n}(\mathbb{R})$ of $n\times n$ matrices over $\mathbb{R}$.

Which of the following best describes $\textrm{Mat}_{n}(\mathbb{R})$ under matrix multiplication?

A

Associative, commutative

B

Not associative, not commutative

C

Associative, not commutative

D

Not associative, commutative