(a) The board of adjustment shall adopt rules necessary to the conduct of its affairs and in keeping with this chapter. Meetings shall be held at the call of the chairman and at such other times as a majority of the board of adjustment may determine. The chairman or, in his absence, the acting chairman may administer oaths and compel the attendance of witnesses. All meetings shall be open to the public.

(b) The board of adjustment shall keep minutes of its proceedings, showing the vote of each member upon each question or if absent or failing to vote indicating such fact, and shall keep records of its examinations and other official actions, all of which shall be public records and shall be immediately filed in the office of the city clerk for the board of adjustment.