Problem 1: SupposeGis a group with the property thatagb=cgdalways implies thatab=cd. Prove thatGis abelian.

What does this question mean? Isga special element ofG,or any old element? Supposegis the identity (in which caseab=cdanyway). How does one prove this?

Problem 2: SupposeGis a finite abelian group in which no non-identity is equal to its own inverse. Determine the product of all the elements ofG.

How can I do the entire table? It could have thousands (literally!) of entries (or more). How do I know whatatimebequals? I don't get it.