1. For an arbitrary binary operation * on a set N, a * a = a ∀ a ∈ N.
2. If * is a commutative binary operation on N, then a * (b * c) = (c * b) * a

solution:

(i) Given: * being a paired procedure on N, is characterized as a * a = a ∀ a ∈ N

Here activity * isn’t characterized, subsequently, the given assertion isn’t correct.

(ii) Operation * being a paired procedure on N. c * b = b * c

(c * b) * a = (b * c) * a = a * (b * c)

Accordingly, a * (b * c) = (c * b) * a, subsequently the given assertion is valid.