Define a binary operation * on the set `A={0,\ 1,\ 2,\ 3,\ 4,\ 5}` as `a*b=a+b(mod\ 6)` . 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 `adot`

Explanation

`\ \^{+}6 \ \ \ \ \ \ 0 \ \ \ \ \ 1 \ \ \ \ \ \ 2 \ \ \ \ \ \ 3 \ \ \ \ \ \ 4 \ \ \ \ \ \ 5`


`\ 0 \ \ \ \ \ \ 0 \ \ \ \ \ 1 \ \ \ \ \ \ 2 \ \ \ \ \ \ 3 \ \ \ \ \ \ 4 \ \ \ \ \ \ 5`


`\ 1 \ \ \ \ \ \ 1 \ \ \ \ \ 2 \ \ \ \ \ \ 3 \ \ \ \ \ \ 4 \ \ \ \ \ \ 5 \ \ \ \ \ \ 0`


`\ 2 \ \ \ \ \ \ 2 \ \ \ \ \ \ 3 \ \ \ \ \ \ 4 \ \ \ \ \ \ 5 \ \ \ \ \ \ 0 \ \ \ \ \ 1`


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