Hint for Section G.1 Question 3

3. Check the group axioms:

• closure under multiplication modulo 6: if you multiply any pair of elements in Z₆-{0}, is the result also an element of Z₆-{0}?
• associativity: does (a × b) × c = a × (b × c) for a, b, c Z₆-{0}?
• identity: do we have e Z₆-{0} such that e × a = a = a × e for all a Z₆-{0}?
• inverse: for all a Z₆-{0}, do we have an a^-1 such that a × a^-1 = e = a^-1 × a?

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