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Let S= {0, 1, 2, 3, 4, 5, 6, 7} and ⊗ denote multiplication modulo 8, that is, x ⊗ y= (xy) mod 8

Prove that ( { 0, 1}, ⊗) is not a group.

Write 3 distinct groups (G, ⊗) where G ⊂ S and G has 2 elements.
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A)1 is the identity element.inverse doesn't exist for zero.so it is not a group

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Then how can A be a group?
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Sorry I can't get your question.Actual question is to prove A is not a group.I also proved it.Is there is any mistake?
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Sorry. i misread the question and didn't see the A, B separation in answer.
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it's ok :)