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If G is a group and a belongs to G such that a^2=a, then a is equal to
1) zero element
2) inverse of each element
3) identity element
4) none of these?
Most Upvoted Answer
If G is a group and a belongs to G such that a^2=a, then a is equal to...
Explanation:

Given:
- G is a group
- a belongs to G
- a^2 = a

Proof:
- Let's prove that a = 1 (identity element)

Proof by Multiplication:
- Multiplying both sides of the equation a^2 = a by a^-1 (inverse of a), we get:
a * a^-1 = a * a
a * a^-1 = a (as a^2 = a)
This implies a^-1 = 1 (identity element)

Conclusion:
- Therefore, if a^2 = a, then a is the identity element in the group G.
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If G is a group and a belongs to G such that a^2=a, then a is equal to 1) zero element 2) inverse of each element 3) identity element4) none of these?
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