1. Which of the following is a group? To find the identity element, which in these problems is an ordered pair (e1, e2) of real numbers, solve the equation (a,b)*(e1, e2)=(a,b) for e1 and e2. 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)-1=(aa-1-bb-1,ab-1+ba-1) Unless I'm really screwing up here, I think this implies that e1-e2 is the first value, which would be equivalent to e1. However, I don't know how to resolve the ab-1+ba-1) part. 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.