Hello, I am having trouble understanding groups in my group theory class. I am not confident on how to approach the following question: I know that y4 = u. So then, g = xy4 = xu = x. Then g2 = x2 = u which is what I am trying to prove. Now if i = 1 then, g = xy. Then g2 = xy xy = x yx y = x xy-1 y. Then xx y-1y = x2 y-1y = u y-1y since x2 = 2. Then u y-1y = u u = u since y-1y = u. First question: Is the work I have completed so far correct? Second question: Do I need to prove this in a case by case basis? That is, I would think that I would have to prove this for i = 1,2,3,4. Since I have already completed 1 and 4, I would have to do cases in which i = 2,3. Correct? This may seem elementry, but like I stated above, my confidence in answering such questions is not great. And my understanding of the material is very weak. Any comments, input, help is appreciated. Thankyou.