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

Forming the operation table

It is clear from the operation table that 0 is the identity element for the given operation.
inverse of 1 = 5 = 6 - 1
inverse of 3 = 3 = 6 - 3
inverse of 4 == 2 = 6 - 4
inverse of 5 = 1 = 6 - 5
`therefore` 6- a is the inverse of `a ne 0` if a is the element of give get .