Would you give her your password?

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Say that you caught your boyfriend/girlfriend in contact with their ex-bf/gf that they cheated on you with, not only cheated on you with, but also promised you that there would be no more contact.... If this happened to you, would you want to know your bf/gf's password for their email? Would it be wrong to ask for it? or Would it be wrong of them not to give it to you? Obviously seeing that there are trust issues, shouldn't the person that was caught in contact with the ex, feel obligated to make his/her gf feel at ease by giving them their password? What would you do if you were denied that password? Especially after you offer to give them yours?