A set S with the operation * is an Abelian group if the following five properties are shown to be true:

● closure property: For all r and t in S, r*t is also in S

● commutative property: For all r and t in S, r*t=t*r

● identity property: There exists an element e in S so that for every s in S, s*e=s

● inverse property: For every s in S, there exists an element x in S so that s*x=e

● associative property: For every q, r, and t in S, q*(r*t)=(q*r)*t

A. Prove that the set G (the fifth roots of unity) is an Abelian group under the operation * (complex multiplication) by using the definition given above to prove the following are true:

1. closure property

2. commutative property

3. identity property

4. inverse property

5. associative property