The provisions of § 31-7-1 shall be operative as to a nonresident owner or operator only to the extent that, under the laws of his or her residence or licensing country, state, territory, or district, like privileges are granted to motor vehicle owners resident of and registered under the laws of this state or operators licensed under the laws of this state. The division of motor vehicles shall finally determine the extent of the privileges granted to nonresident owners and operators of motor vehicles in the registration of motor vehicles and licenses of operators. The division of motor vehicles is authorized 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 with respect to all fees or taxes imposed by this state and by any other state or the District of Columbia on motor vehicles, on the operation of motor vehicles, or on any transaction incident to the operation of motor vehicles.