 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2023/paper-2/8/a/i/solution

(0 * 0) * 1 = - 1

but

0 * (0 * 1) = 1

. Thus it violates the group axioms and is not a group. It has a right identity

0

, but no element can be a two-sided identity element.

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