That will work, we call them Cali corners. But for a basement you can just put a stud at the inside corner of each wall and tie it in with a block
I did research and found the cali corner, I did it that way so I can get wall insulation all the way to the corner. The way I spaced everything out takes into account the 1/2" thickness of drywall, so the bottom wall drywall needs to be done first, and then the left wall drywall can be butt up to the bottom wall. Quick question: Should there be no gap between the drywall pieces on the bottom and left, correct? The way I show it, and the way everything is dimensioned, it takes into account no gap between the two pieces of drywall in the corner.That will work, we call them Cali corners. But for a basement you can just put a stud at the inside corner of each wall and tie it in with a block