The governor is authorized, with the advice of the board, to enter into reciprocal agreements on behalf of the state, with the appropriate authorities of any state in the United States of America, or of the District of Columbia, or of any province in the dominion of Canada, with respect to all fees or taxes imposed by this state and by any other state, or the District of Columbia, or any province of Canada, on motor vehicles, or on the operation of motor vehicles, or upon any transaction incident to the operation of motor vehicles. It shall be the duty of the board to study and advise the governor with respect to all matters affecting any reciprocal agreements.