Let * be a binary operation on the set Q of rational numbers as follows:
(i) a * b = a ā b (ii) a * b = a2 + b2
(iii) a * b = a + ab (iv) a * b = (a ā b)2
(v) (vi) a
*
b =
ab2
Find which of the binary operations are commutative and which are associative.