Let S = R-{-1}. Define an operation on S by a*b = a + b + ab, a, b € S. (6.1) Show that S is closed under the operation *. (6.2) What is the identity in S under *? (6.3) What is the inverse of a € S under *? (6.4) Assuming that is associative, show that (S, *) is an abelian group. (6.5) Solve for x in the equation 1 * x = 2.

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