I cut out the same size square in sheetrock, but I did not cut it all the way through the sheetrock.  Keep the top layer of sheetrock paper about 2-3 inches.  It is a little bit of work to get it to look like this but it peels off with some effort.  Next step is to place mud around the square hole in the ceiling.  Then put the square in the square hole with the paper around it. The mud will act as a glue to keep it in place. Use a trowel to smooth out the mud so it does not clump up.