Oya Paka and two business associates formed a corporation called Paka Corp. for the purpose of selling computer services. Oya, who owned $50$ percent of the corporate shares, served as the corporation$$s president. Oya wished to obtain a personal loan from her bank for $$250,000,$ but the bank required the note to be cosigned by a third party. Oya cosigned the note in the name of the corporation. Later, Oya defaulted on the note, and the bank sued the corporation for payment. The corporation asserted, as a defense, that Oya had exceeded her authority when she cosigned the note on behalf of the corporation. Had she? Explain fully.