Which is the correct converse for the pictured question (so you can see the exact wording)?

Converse One: Take the converse of the statementagb=cgdalways implies thatab=cd. That is:

SupposeGis a group with the property thatab=cdalways impliesagb=cgd. Prove or disproveGis abelian.

This seems like a kind of silly statement, and I see no way to prove it. The only way to makeab=cdis ifa=candb=dor ifa=b=c=d.

Converse Two: Take the converse of the question. That is:

Suppose that G is an abelian group. Prove thatGhas the property thatagb=cgdalways impliesab=cd.

Which is too easy to be part (b) of this question. If G is abelian andagb=cgd, then we have

agb=cgd

gab=gcd

g^{-1}gab=g^{-1}gcd

ab=cd

Which means thatGhas that property.

TIA.