(a) The Secretary shall decide all questions of law and fact necessary to a decision by the Secretary under a law that affects the provision of benefits by the Secretary to veterans or the dependents or survivors of veterans.

Subject to subsection (b), the decision of the Secretary as to any such question shall be final and conclusive and may not be reviewed by any other official or by any court, whether by an action in the nature of mandamus or otherwise. (b) The second sentence of subsection (a) does not apply to - (1) matters subject to section 502 of this title; (2) matters covered by sections 1975 and 1984 of this title; (3) matters arising under chapter 37 of this title; and (4) matters covered by chapter 72 of this title.