Decide which of the following sets are groups under the given operations: (i) the set Q of rational numbers, under multiplication; (ii) the set of non-zero complex numbers, under multiplication; (iii) the non-zero integers, under multiplication; (iv) the set of all functions from {1, 2, 3} to itself, under composition of functions; (v) the set of all real numbers of the form a + b √ 2 where a and b are integers, under addition; (vi) the set of all 3 × 3 matrices of the form