Which landmark case gave the U.S. Supreme Court the authority to invalidate an act of Congress as unconstitutional?

The case that established the authority of the U.S. Supreme Court to invalidate acts of Congress as unconstitutional is Marbury v. Madison. This landmark decision, decided in 1803, was significant for the doctrine of judicial review, which allows the judiciary to review legislative and executive actions and determine their constitutionality.

In Marbury v. Madison, the Court, led by Chief Justice John Marshall, asserted that it is emphatically the province and duty of the judicial department to say what the law is. This ruling confirmed the power of the Supreme Court to declare laws passed by Congress and actions taken by the executive branch unconstitutional, thereby reinforcing the system of checks and balances essential to the U.S. government.

The other cases listed, while significant in their own rights, do not establish this fundamental principle of judicial review. Brown v. Board of Education addressed racial segregation in public schools. Roe v. Wade focused on a woman's right to privacy regarding abortion. Miranda v. Arizona dealt with the rights of individuals in police custody. None of these cases specifically conferred the power of judicial review to invalidate congressional legislation.