(a) Except as otherwise provided, the supreme court shall have jurisdiction and powers as follows:
(1) To hear and determine all questions of law, or of mixed law and fact, which are properly brought before it by application for a writ of certiorari to the intermediate appellate court or by transfer as provided in this chapter;
(2) To answer, in its discretion, any question of law reserved by a circuit court, the land court, or the tax appeal court, or any question or proposition of law certified to it by a federal district or appellate court if the supreme court shall so provide by rule;
(3) To exercise original jurisdiction in all questions arising under writs directed to courts of inferior jurisdiction and returnable before the supreme court, or if the supreme court consents to receive the case arising under writs of mandamus directed to public officers to compel them to fulfill the duties of their offices; and such other original jurisdiction as may be expressly conferred by law;
(4) To issue writs of habeas corpus, or orders to show cause as provided by chapter 660, returnable before the supreme court or a circuit court, and any justice may issue writs of habeas corpus or such orders to show cause, returnable as above stated;
(5) To make or issue any order or writ necessary or appropriate in aid of its jurisdiction, and in such case, any justice may issue a writ or an order to show cause returnable before the supreme court; and
(6) To make and award such judgments, decrees, orders and mandates, issue such executions and other processes, and do such other acts and take such other steps as may be necessary to carry into full effect the powers which are or shall be given to it by law or for the promotion of justice in matters pending before it.
(b) All cases addressed to the jurisdiction of the supreme court or of the intermediate appellate court shall be filed with the clerk of the supreme court as provided by the rules of court. The clerk shall maintain the record of each case whether addressed to the jurisdiction of the supreme court or the jurisdiction of the intermediate appellate court.