Question: Let S = R* R. Define the binary operation on S by (u, v) (x, y) = (ux, vx + y). Prove

Let S = R* × R. Define the binary operation ◦ on S by (u, v) ◦ (x, y) = (ux, vx + y). Prove that (S, ◦) is a non-abelian group.

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