"Can I glue the sheet to the cement board? What should I use?"

1. Yep
2. Double coated contact cement

I wouldn't recommend cement board for a laminate substrate.
Laminate works with exterior plywood. Tile works with cement board.
Ron

The cement alphonse suggested is the way to go. No matter what you glue the laminate to, there is a technique to be followed or you'll have a mess on your hands. I suggest that a newbie to the process plan on the actual size of the back splash to be smaller than the gluing project so you can trim it up compensating for "hangover" laminate or crooked bonding. This happens to even the most experienced at times. You and hubby practice many dry runs before doing it.

Ok, I am giving this task up. I think I will be tiling. I do not feel confortable to use glue and mastic etc on a 8'x 30" (2 panel) surface...I have plenty of tiles and I want to do something fast and not too messy (I have 2 kids and a full time job). Thanks to all of you for the great answers!!!

It is laminate on cement board, use a construction adhesive like liquid nails and it will stay.

Unless someone will be walking on the wall.. One little dab at each corner would hold it and if you want to remove it later it would be easy.

Basement laundry room, I assume you are sure the wall doesn't leak and the wall is dry. For laminant panels you can even skip the cement board and use a dab of glue at each corner on the studs.