Good question. I never thought of it before. Wiki has an answer at http://en.wikipedia.org/wiki/Pressure

"Pressure is a scalar quantity. It relates the vector surface element (a vector normal to the surface) with the normal force acting on it. The pressure is the scalar proportionality constant that relates the two normal vectors:"

That is, both F and A are vectors - collinear and facing opposite directions. I don't remember learning this in any of my classes - but it's been 30 years since I took mechanics.