I need to prove or disprove the following:
1. Let and . A is a Group.
2. Let and . A is a Group.
both with the operation:
My intuition says 1 is true and 2 is false (the unit element in 1 is , and with simple algebra I can find the inverse element for a given element ), but I'm not sure about 2.
Can someone please give me some help with it?
Thanks in advanced!