State whether the following statements are true or false. Justify:

(i) For an arbitrary binary operation * on a set N, a * a = a ∀ a ∈ N.

(ii) If * is a commutative binary operation on N, then a * (b * b ) = (c * b) * a.

(i) For an arbitrary binary operation * on a set N, a * a = a ∀ a ∈ N.

(ii) If * is a commutative binary operation on N, then a * (b * b ) = (c * b) * a.