Some help with the following proof would be great:

Zn is the set of integers modulo n

Fix an integer n >= 2. Addition and multiplication on Zn are commutative, associative, and distributive.Prove that the set Zn has an additive identity, a multiplicative identity, and additive inverses.

Addition and multiplication are defined in the following way. If a ≡ a' (mod n) and b ≡ b' (mod n) then

a+b ≡ a' + b' (mod n) and ab ≡ a'b' (mod n)

and so [a] + [b] = [a+b] and [a] * [b] = [ab]

Any help is appreciated!