the additive inverse and identity element

just want to make sure that my thinking is on the right track here. we are working with abstract algebra, more specifically we are working with groups. so the + symbol should have a circle around it:

Given (a,b)E of Z x Z* [a,b are elements of integers times integers with no zeros]

show that [(-a,b)] is an additive inverse of [(a,b), that is [(a,b)] + [(-a,b)]=[(0,1)]

What I think I have to do:

show that [(a,b)]+[(-a,b)] = [(-a,b)]+[(a,b)] (or in relation to)

which will give the identity element [(0,1)]

so using the communitive law:

[ab + b-a,bb] = [(0.1)]

again note that the + symbol shoul have a circle around it. Any advice would be good. If you need clarification on anything, let me know. Thank you.