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Define a binary operation * on the set {...

Define a binary operation * on the set `{0, 1, 2, 3, 4, 5}` as `a*b = { a + b , if a+ b < 6 a+b-6 , if a+bge6`. Show that zero is the identity for this operation and each element 'a' of the set is invertible with (6-a) being the inverse of a.

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