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Answer:
Alexander Hamilton belonged to the Federalist Party, which supported the idea of a strong central government. He thought that the federal government should be able to keep a strong army and navy, to raise taxes, and to have good relations with Great Britain.
James Madison was on the opposite side. He was a member of the Democratic-Republican Party. This party favored a weak central government, and favored state and local power.
The biggest rift between Hamilton and Madison came when the issue of a federal bank came up in Congress. Hamilton wanted to create a Central Bank to take on the debts of the states, and to fund future programs and armies, Madison, as anti-federalist, naturally opposed this idea.
This rift was solved with the Compromise of 1790. The southerners, including James Madison, agreed to the creation of a national bank in exchange for having the new capital in southern territory (Washington D.C.).
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