Solve Binary Operations Question: Prove Isomorphism

[Jumblebee]

So I have really been struggling with this question. The original question said: The map $$\varphi$$:Z->Z defined by $$\varphi$$(n)=n+1 for n in Z is one to one and onto Z. For (Z, . ) onto (Z,*) (i am using . for usual multiplication) define * and show that * makes phi into an isomorphism.
I know that the operation must be m*n=mn-m-n+2. But I get stuck in proving that the operations are preserved. When I do $$\varphi$$(m.n) i get mn+1. and i can't get $$\varphi$$(m). $$\varphi$$(n) to work. I think I am doing something wrong. Can anyone help?

 

[Jumblebee]

Never mind! i just got it to work!