State whether the following statements are true or false. justify.
(i) for an arbitrary binary operation * on a set n, a * a = a , for all a * n.
(ii) if * is a commutative binary operation on n, then a * (b * c) = (c * b) * a

(i) false;
Let be N = { 0, 1 , 2}; x * y = x + y => a * a = 2a ∈ { 0, 2 , 4}, which is not a( just for a = 0);

(ii) true;
b * c = c * b => a * ( b * c ) = a * ( c * b );                  (1)
                   but, a * ( c * b ) = ( c *  b ) * a;               (2)

(1) and (2) => a * (b * c) = (c * b) * a.