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Proving Set With Nth Root

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

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