Mounting Quartz slab on drywall or cement

I am thinking of mounting a quartz slab (3/4" thick) that extends to the ceiling behind my 36" range top and range hood (chimney style).

I was wondering if it is secure enough to mount it on drywall, or should I use a cement board behind the quartz slab.

Below is a picture of approximately where I am mounting the quartz (vertical drywall).