Final answer:
No, the Governor of New York cannot invade Canada with the National Guard, as the power to declare war is reserved for the President and Congress, under Article I, Section 8 and Article II, Section 2 of the U.S. Constitution.
Step-by-step explanation:
No, as Governor of New York, Andrew Cuomo does not have the authority to take the New York National Guard and invade Canada. The action of invading another country is a power reserved for the federal government, specifically the President of the United States, with the consent of Congress. This is addressed in the U.S. Constitution, Article I, Section 8, which grants Congress the power to declare war, and Article II, Section 2, which designates the President as the Commander-in-Chief of the military. The use of the National Guard for state purposes, such as responding to severe weather or civil unrest, is within the gubernatorial powers, but deploying troops for offensive military actions against another sovereign nation is not.