If G is a group and a belongs to G such that a^2=a then a is equal to?

Question

Answer

Identifying the Element of the Group G
Given that a^2 = a, we need to determine the value of a in the group G.

Finding the Value of a
Since a^2 = a, we can rewrite this equation as a^2 - a = 0. Factoring out an 'a' from this equation, we get a(a - 1) = 0. This implies that either a = 0 or a - 1 = 0.
If a = 0, then a^2 = 0^2 = 0, which satisfies the given condition.
If a = 1, then a^2 = 1^2 = 1, which also satisfies the given condition.
Therefore, the possible values for a in the group G are 0 and 1.

Conclusion
In conclusion, the element a in the group G, such that a^2 = a, can be either 0 or 1. These values satisfy the given condition and are valid elements of the group.

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