can you install cement backer board over old sheetrock?
You can but it will bump all the walls in by the depth of the cement board. Plus, if it is a bath or kitchen, then the cement board will encroach on the tub and/or sink, especially considering the extra depth the tile will add. I always remove the old sheetrock because mold can easily be growing in there if it is in a room prone to dampness like a bath or kitchen. Also, the cement board will be a much sturdier mount if it is directly on the studs.