You may start with that, i.e. equating the products hk and kh, the only interesting equation you should get is (dashed symbols are components of k) then h is in the center iff holds for any , so you deduce that . You can see now why .

For the second question, it's easy to check that the order of any element of divides 3. So the order of any element of divides 3 i.e. it's not cyclic. Conclude.