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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?
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.
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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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? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about 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? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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?.
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? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about 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? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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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