NTA UGC NET Dec 2023 Paper-2
February 6, 2024GATE 2018
February 7, 2024Question 9018 – GATE 2010
Consider the set S = {1, ω, ω2}, where ω and ω2 are cube roots of unity. If * denotes the multiplication operation, the structure (S,*) forms
Correct Answer: A
Question 4 Explanation:
A Group is an algebraic structure which satisfies
1) Closure
2) Associativity
3) Have Identity element
4) Invertible
1) Closure
2) Associativity
3) Have Identity element
4) Invertible
Over ‘*’ operation the S = {1, ω, ω2} satisfies the above properties.
The identity element is ‘1’ and inverse of 1 is 1, inverse of ‘w’ is ‘w2‘ and inverse of ‘w2‘ is ‘w’.
A group
A ring
An integral domain
A field