Final answer:
The most significant check that the judicial branch can wield against the other two branches of government is invalidating laws and executive decisions through judicial review.
Step-by-step explanation:
The most significant check that the judicial branch can wield against the other two branches of government is invalidating laws and executive decisions. This power is known as judicial review, and it allows the courts to refuse to apply a state or federal law that violates the U.S. Constitution. One of the most important cases that established this power is Marbury v. Madison in 1803.
Judicial review serves as a crucial check on the legislative and executive branches. By declaring laws or actions unconstitutional, the courts can prevent the other branches from overstepping their constitutional authority. This power ensures that no branch of government becomes too powerful, allowing for a system of checks and balances to exist.
Additionally, the judicial branch can also check the other branches through their authority to interpret laws and the Constitution. Their decisions can impact the executive and legislative branches, influencing the direction of policies and actions taken by these branches.