(a) If a person acting, or purporting to act, as a representative signs an instrument by signing either the name of the represented person or the name of the signer, the represented person is bound by the signature to the same extent the represented person would be bound if the signature were on a simple contract. If the represented person is bound, the signature of the representative is the "authorized signature of the represented person" and the represented person is liable on the instrument, whether or not identified in the instrument.
(b) If a representative signs the name of the representative to an instrument and the signature is an authorized signature of the represented person, the following rules apply:
(1) If the form of the signature shows unambiguously that the signature is made on behalf of the represented person who is identified in the instrument, the representative is not liable on the instrument.