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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