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During the forty years of wandering in the wilderness, the tribe of Judah would always encamp to the east of the Tabernacle and would march in the first rank, presumably to the left of the tribes of Issachar and Zebulun, which would encamp and march next to Judah.
The inheritance of Judah turned out to be a fairly sizeable amount of land in the southern portion of the promised land, a good position to be in since invaders really came from the desert to the south.
When the kingdom of Israel split in two after the death of Solomon and under the harsh terms set up by his son Rehoboam, it was the tribe of Judah along with Benjamin that made up the southern kingdom, Judah. A descendant of David, and therefore Judah, continued to rule on the thrown until its fall several hundred years later.