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Define a binary operation on R 2 − {(0, 0)} by (a, b) · (c, d)...

Define a binary operation on R 2 − {(0, 0)} by (a, b) · (c, d) = (ac − bd, ad + bc). Prove that (R 2 − {0}, ·) is an abelian group. (You do not need to prove that the operation is closed.)

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