Decide whether or not the modulo system forms a group.
-{1, 2}; multiplication modulo 3
A) Not a group
B) Group

Question

Quizplus · Accepted Answer

The modulo system forms a group because it satisfies the four group axioms:1. Closure: For any two elements a and b in the set, their product a * b is also in the set.2. Associativity: For any three elements a, b, and c in the set, their product (a * b) * c is equal to a * (b * c).3. Identity element: There exists an element e in the set such that for any element a in the set, a * e = e * a = a.4. Inverse element: For each element a in the set, there exists an element b in the set such that a * b = b * a = e, where e is the identity element.

Decide Whether or Not the Modulo System Forms a Group