Decide whether or not the modulo system forms a group. {0, 1}; multiplication modulo 2

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Decide whether or not the modulo system forms a group. {0, 1}; multiplication modulo 2

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Before I start, what do you think, and why?
there are three parts to test, (i) associativity, (ii) existence of an identity, and (iii) every element has an inverse relative to the given operation
now, if you think the modulo system is not a group, which of the three parts (i) associativity, (ii) identity, or (iii) inverse will fail?

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