Define a binary operation ∗ on the set {0, 1, 2, 3, 4, 5} as , if 6 6 if 6 a b a b a b a b a b ⎧ + + < ∗ = ⎨ + − + ≥ ⎩ 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.

Define a binary operation ∗ on the set {0, 1, 2, 3, 4, 5} as ,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.