Let $G = mathbb{Q} - {2}$ and define this operation on $G$: $a * b = ab - 2a - 2b + 6$ where the operations on the right side of the equal sign are the usual addition and multiplication in $mathbb{Q}$. Show $G$ is an abelian group. What is the identity? Find a formula for the inverse of $a$? What is the inverse of $frac{3}{2}$?
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The following Cayley table represents the multiplication of the group G = {a, b, c, d, f} under *: (a) Find the identity of G. (b) Find the inverse of b. (c) Solve for x in the following equation: a^-1x = b.
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