Incorrect Answer.
From the two statements about common knowledge we know the following formulas,
C(a 
b),
C(KAb KA 
b),
C(KBa KB a).
Suppose that a is false. KBa KB a is true, so in this case KB a is true, ie. B would know that a was false. But B knows that a b is true (from common knowledge), so would be able to deduce that b is true, ie. B would know that her own husband is unfaithful. Given the truthfulness of B, she would have also stated this fact, but she stated she did not know. Therefore our assumption that a is false must be false, ie. a must be true. I deduced this simply from the statements of common knowledge, so A would be able to replicate this deduction, ie. A would also be able to deduce her husband is unfaithful, and would state this in her answer.
Back to Question.