Proofs to the conjectures made by Jing and Hassibi on having fully diverse (3/spl times/3) SU(3) and AB unitary space-time codes are presented in this correspondence. We first prove that the SU(3) codes are fully diverse if and only if the design parameters P,Q,R, and S are all odd integers, and in addition, are relatively prime. For the type I AB codes, it is shown that full diversity can be achieved if and only if the integers P,Q,R, and S are relatively prime. Finally, we show that such condition is also sufficient for having fully diverse type II AB codes.