Let A and B be oversvables, suppose the simultaneous eigenkets of A and B {|, b>} form

Question:

Let A and B be oversvables, suppose the simultaneous eigenkets of A and B {|α’, b’>} form a complete orthonormal set of base kets. Can we always conclude that [A, B] = 0? If your answer is yes, prove the assertion, if your answer is no, give a counterexample.