(a) It shall be the duty of the Collector to keep in his office account books, in which shall be entered:
(1) The dates of payment of all taxes;
(2) The amounts paid;
(3) The names of the persons by whom payment has been made;
(4) The years paid for;
(5) The property paid on; and
(6) The names of the persons to whom assessed.
(b) His books shall at all times be open to the inspection of any officer who may be authorized by the Mayor of the District of Columbia to examine the same.