Jay-Z is keeping a close eye on his multimillion dollar NBA investment -- showing up to a Brooklyn construction site yesterday to check out the future home of the Nets ... and even trying his hand at some hard labor.

The rapper toured the dirt-filled construction yard on Friday -- known as Barclays Stadium -- to take a gander at where his Brooklyn Nets will earn their stripes ... as in black and white, 'cause the team's colors just changed too.