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

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


`a * b={(a+b,if a+b<6),(a+b-6,if a+b geq 6):}`


To check if zero is the identify, we see that `a * 0=a+0=a`

for all `a in x` and also `0 * a=0+a=a` for `a in x`

Given `a in X, a+0<6` and also `0+a<6`

`rightarrow 0` is the identity element for the given operation.

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