Determine which of the following binary operations on the set N are associative and which are commutative.

(a)  Clearly, by definition a * b = b * a = 1, ∀ a, b ∈ N. Also

(a * b) * c = (1 * c) =1 and a * (b * c) = a * (1) = 1, ∀ a, b, c ∈ N. Hence

R is both associative and commutative.