Question

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 ≠ 0 of the set is invertible with 6 − a being the inverse of a. 

Answer 1

∴a∗0=a=0∗a for all a∈ X
Thus, 0 is the identity element for the given operation *. An element a ∈ X is invertible if there exists b ∈ X such that a * b = 0 = b * a.