Modulo Definition of Addition and Multiplication
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!