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**1. Which of the following is a group?**

To find the identity element, which in these problems is an ordered pair (e

To find the identity element, which in these problems is an ordered pair (e

_{1}, e_{2}) of real numbers, solve the equation (a,b)*(e_{1}, e_{2})=(a,b) for e_{1}and e_{2}.**2. (a,b)*(c,d)=(ac-bd,ad+bc), on the set ℝxℝ with the origin deleted.**

**3. The question also asks for you to find the inverse and I think implicitly for associativity and then for commutativity. I've got the other three down, but the identity axiom is giving me trouble.**

(a,b)*(a,b)

Unless I'm really screwing up here, I think this implies that

(a,b)*(a,b)

^{-1}=(aa^{-1}-bb^{-1},ab^{-1}+ba^{-1})Unless I'm really screwing up here, I think this implies that

__e__is the first value, which would be equivalent to e_{1}-e_{2}_{1}. However, I don't know how to resolve the__ab__part.^{-1}+ba^{-1})I think I've been dropped from this class for a lack of prerequisites, but I think I'm still going to try and finish the class nonetheless.