Determined if the following is an equivalence relation, if so describe the equivalence class.
The relationship [tex]C[/tex] on a group [tex]G[/tex], where [tex]aCb[/tex] iff [tex]ab=ba[/tex]
The Attempt at a Solution
So i know there's 3 things to check: reflexive condition, symmetric condition, and the transitive condition.
The 1st two passed just by inspection, but I'm really stuck on the last one.
So if [tex]ab=ba[/tex] and [tex]bd=db[/tex] on a group [tex]G[/tex]does that imply [tex]ad=da[/tex]? That's how i set it up but I can't find how to (dis)prove it.