First, do you mean to define ?
I think that your first step is to determine the kernel of . If , what can be said about and ?
[spoil]Clearly if then since since and similarly . Conversely, suppose that $latex F(x,y)=(S,T)[/tex] then . But, note that since and so . Similarly and so . Combining these we get [/spoil]
EDIT: I can't figure out how to hide it...so work on the honor code haha