A binary operation * on the set {0,1,2,3,4,5} is defined as: `a`*`b={a+b ,a+b-6"\ \ \ \ if\ "a+b<6"\ \ \ if"\ a+bgeq6` 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 given operation `**` on `X` is defined as:

`a**b={a+b if a+b<6`

                 
`a+b-6 if a+b≥6}`


An element `einX` is the identity element for the operation `**`, if
`a**e=a=e**a` for `a in X`.

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