Let * be a binary operation on `Z` defined by `a*b=a+b-4` for all `a ,\ b in Zdot` Find the identity element in `Zdot` (ii) Find the invertible elements in `Zdot`

Explanation

identity element

`a * e = a` and `e * a = a`, `forall a in Z`

` a + e – 4 = a` and `e + a – 4 = a, forall a in Z`

` e = 4, forall a in Z`

Thus, `4` is the identity element in `Z` with respect to `*`.



`a * b = e = b * a`
`a * b = e` and `b * a = e`

` a + b – 4 = 4` and `b + a – 4 = 4`
...