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` OR A binary operation * on the set `{0,1,2,3,4,5}` is defined as `a*b={a+b ,ifa+b<6a+b-6,ifa+bgeq6` Show that zero is the identity for this operation and each element a of set is invertible with `6-a ,` being the inverse of a.

Explanation

Let `X={0,1,2,3,4,5}`.

The operation * on `X` is defined as:


`a * b=` `{(a+b if a+b < 0),(a + b – 6 if a + b >= 6):}`


An element `e in X` is the identity element for the operation *, if `{a}^{*} {e}={a}={e}^{*}` `a forall a in X`

For `a in X` we observed that


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