How did President George Washington's most valuable Cabinet members Alexander Hamilton and Thomas Jefferson disagree economically as pro-industry/manufacturing and pro-agriculture/farming respectively? How did friends-turned-rivals John Adams and Thomas Jefferson disagree politically as Federalist and Democratic-Republican President respectively?

The correct answer to this open question is the following.

Alexander Hamilton and Thomas Jefferson disagreed economically as pro-industry/manufacturing and pro-agriculture/farming in that Alexander Hamilton, Secretary of the Treasury, believed the support of the US industry and trade would be the foundation of the economic success of the country. On the other hand, Thomas Jefferson firmly believed the opposite. He thought that the strength of the United States relied on agriculture. Yes, the agricultural tradition based on American farmers.

Indeed, when George Washington was the President of the United States, the disagreements between Jefferson and  Hamilton over the interpretation of the Constitution and the best political and economic system for the country ended up with the creation of political parties, something that Washington was in total opposition of, because he considered this could represent the division of the country from within.

Something similar happened with the relationship of

John Adams and Thomas Jefferson, that during the Constitutional Convention of Philadelphia were the best of friends, while during the presidential times of both, they disagreed politically as Federalist and Democratic-Republican President respectively. Their vision of politics, made them be confronted many times.

i don't get what you mean

explanation:

this is a good question! i'll do some research and come back when i have the answer!