(a) Except as provided in subsection (b) of this section, if a deposit is made in a bank to the credit of a fiduciary, the bank is authorized to pay the amount of the deposit or any part of it on the check of the fiduciary, signed with the name in which the deposit is entered, without being liable to the principal, unless the bank pays the check with actual knowledge that the fiduciary is committing a breach of the obligation as fiduciary in drawing the check or with knowledge of the facts that the action of the bank in paying the check amounts to bad faith.

(b) If a check is payable to the drawee bank and is delivered to the bank in payment of or as security for a personal debt of the fiduciary to it, the bank is liable to the principal if the fiduciary in fact commits a breach of the obligation as fiduciary in drawing or delivering the check.