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Abstract Algebra

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Decomposing a Matrix Group

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Let $G$ be the group (under addition) of $2\times 2$ matrices with real coefficients.

Which of the following groups are isomorphic to $G$?

Select ALL that apply.

A

$\mathbb{R}\times \mathbb{R}$

B

$\mathbb{R}\times \mathbb{R}\times \mathbb{R}\times \mathbb{R}$

C

$\mathbb{R}\times \mathbb{C}$

D

$\mathbb{C}\times \mathbb{C}$

E

$\mathbb{C}$