Is the set of three cube roots of 1 a multiplicative group? Prove

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The cube roots of 1 are `{1,-1/2+3/2i,-1/2-3/2i}`

In order for this set to be a group under multiplication it mustobey the following axioms; closure, associativity, the existence of a unique identity, and every element must have a unique inverse.

The given set is not a group as it is not closed under multiplication.

`(-1/2+3/2i)(-1/2-3/2i)=5/2` which is not an element of the set.

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