Homomorphism 

See the attached file. 

Only one of the maps is an isomorphism in your problem, I guess you may have a typo in (1). If $\phi_1(x,y)=x+y$ and not $xy$, then $\phi_1$ will be an isomorphism. I did both these cases. 

Please note that it took me about 45 minutes to write this solution. Please offer higher amounts in future, otherwise you may not het a reposne from other users.