Let (G, ') denote the set of all 2 x 2 real matrices A with det{. and det {A} € Q (the rational numbers). (a) Prove that (G, ·) is a group with respect to multiplication. (Matrix multiplication is always associative, so you may assume that. But check closure and the existence of an identity element and inverse elements very carefully.) (b) Is this group Abelian? Justify. 2.

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