When a representative signs a document, who is responsible

(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. (2) Subject to subsection (c), if (i) the form of the signature does not show unambiguously that the signature is made in a representative capacity or (ii) the represented person is not identified in the instrument, the representative is liable on the instrument to a holder in due course that took the instrument without notice that the representative was not intended to be liable on the instrument. With respect to any other person, the representative is liable on the instrument unless the representative proves that the original parties did not intend the representative to be liable on the instrument. (c) If a representative signs the name of the representative as drawer of a check without indication of the representative status and the check is payable from an account of the represented person who is identified on the check, the signer is not liable on the check if the signature is an authorized signature of the represented person.