When an object is on an inclined plane the perpendicular gravitational component is equal to the normal force. How can you conclude this?

This is concluded on the basis that the body doesn't show any movement in the direction perpendicular to the incline. If the body has some acceleration in that direction also then we can't say that the normal force is equal to the perpendicular component of the gravity.

This is predicted on the basis of Newton's second law of motion.

so we can usually see from these things that the perpendicular direction has no overall acceleration but we know gravity has a component in this direction so by virtue of newtons third law we must know that the component of gravity in that perpendicular direction must have some equal and opposite force from the slope this is where the normal force comes from. so the normal force is a consequence of the force form the object on the slope not the other way around.