Hint for Section G.1 Question 7

7. Check the group axioms and commutativity:

• closure under *: if a and b are in Z, is a * b also in Z?
• associativity: does (a * b) * c = a * (b * c) for a, b, c Z?
• identity: do we have e Z such that e * a = a = a * e for all a Z?
• inverse: for all a Z, do we have an a^-1 such that a * a^-1 = e = a^-1 * a?
• commutativity: does a * b = b * a for a, b Z?

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