Marbury v. Madison, 5 U.S. (1 Cranch) 137 (1803), was a landmark decision of the U.S. Supreme Court that established the principle of judicial review, meaning that American courts have the power to strike down laws and statutes they find to violate the Constitution of the United States. Decided in 1803, Marbury is regarded as the single most important decision in American constitutional law.
Well that’s an even older decision:
Yes, the supreme Court gave itself that power. To that end the other branches could justifiably choose to not find that to be valid.