(a) That's wrong. People often form a mistaken belief or view about something. They might make an unwarranted assumption about something, or fail to check on the true state of affairs. Generally speaking, if a person enters into a legal transaction such as a contract while they are under a mistaken belief that is their own fault, and provided the other party has not behaved improperly in the circumstances, then the law does not assist the mistaken party. They will be bound by the transaction even if they would not have entered into it had they known the true facts.
In the circumstances of this case, A's mistaken belief does not provide any defence against an action to enforce the sale.