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 `a`.
OR
A binary operation `**` on the set `{0,1,2,3,4,5}` is defined as `a**b={[a+b if a+b<6] , [a+b-6 if a+b >= 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 `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{ }^{*} in X`

For a in` X `we observed that


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