Which political did alexander hamilton belong to? where they supported by common people or aristocracy?

No. While it has become a somewhat widely adopted belief about the man, the notion that Hamilton favored an aristocracy largely arose from attacks and accusations made by his political opponents.

Hamilton did assert in many of his speeches and essays that he believed that leaving significant political power in the hands of common-folk (who at the time were uneducated and ill-informed in policy matters) could result in the making of radical and dangerous decisions. He also believed that government leaders who had considerable wealth of their own were less likely to become corrupt or use their political office for personal gain.

In voicing these concerns, Hamilton certainly brings up valid points - ones that remain valid to this day (consider, for example, how different the recent presidential election outcome would have been if only the wealthy and intellectual elite had a say). Equally valid arguments can certainly be made to the contrary, but claiming that Hamilton favored an aristocracy because of those opinions just isn't fair. Furthermore, Hamilton was vocal about his opinions that those from humbler beginnings with the intelligence and will to achieve should be granted the opportunities to do so, something that isn't likely to happen in an aristocracy.

If you consider Hamilton’s own beginnings as an impoverished, illegitimate child who was ultimately left to his own devices in carving out a life for himself, and ending up having such a profound impact on the nation’s revolution and early development, it's surely hard to believe that he would have held any special favor for aristocrats.

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b: to eliminate competition from other farmers