According to Maxwell's equations, the propagation of light is the cross product of the eletic field vector with the magnmetic field vector. When the propagation is reflected by a mirror surface, does that mean the cross product has been reversed? A X B to B X A (the diected angle between the two vectors have reversedm since the cross product is not commutative)

No, the cross-product has not been reversed. The propagation continues in the direction of the Poynting vector (i.e. in the direction of E x B). Reflection at the surface can be hand-wavingly explained using either the wave or the particle model of light, but a quantum mechanical treatment of the problem is the only way to truly describe what's happening.

Here's the wave-model description: Light propagates because a sinusoidally varying electric field begets a sinusoidally varying magnetic field which in turns begets and electric field which begets... etc. When the light wave reaches the flat metal surface at the back of the mirror, the tangential component of the electric field is forced to zero, causing the wave to reflect. This is analogous to a mechanical wave traveling along a rope or a slinky. The wave propagates because a deformation (a.k.a. strain) results in stored spring energy (a.k.a. a stress), which in turn causes strain in an adjacent portion of the rope or slinky, which causes stress, etc. An animation of such propagation is shown below:

http://www.kettering.edu/physics/drussell/Demos/reflect/pulse.gif

If you tie one end of the rope to a tree or other immovable object, however, you force the strain to zero at that boundary. That results in total reflection of the wave as animated below:

http://www.kettering.edu/physics/drussell/Demos/reflect/hard.gif

Forcing the strain in the rope to zero is analogous to forcing the tangential component of the electric field to zero in the case of a light wave.

How about when the vectors hit the surface? The angle between them, from the view-point of the source, is counter-clockwise: after rebounding, the angle between the vectors, from the view point of the surface, is clockwise (posirive to negative angle).

The angular relationship stays the same. Bear in mind that it's not two separate waves (one electrical and one magnetic) that hit the surface and get reflected (thereby reversing their angular relationship). It's one single electromagnetic wave. A better way to say it would be: it's not the fields that create the wave; it's the wave that creates the fields. Once it leaves the surface, the newly reflected wave's electrical field generates a new magnetic field according to Maxwell's equations, which in turn generates an electric field, etc. etc.

The right-handedness of the relationship (i.e. the relative angle between E and B) is not to be confused with polarization of the wave, which has to do with the absolute angle of the E-field. If the E-field is spinning as a function of time, the B-field will spin right along with it 90 degrees away. The direction of spin DOES get swapped upon reflection, but the right-handedness of E x B is maintained. The two fields continue spinning together in the opposite direction (relative to the propagation direction).

I understand the inter-relationship of the electric field and magnetic field; but I have a hard time not separating the three vectors (E, B, propagation) from each other at the mirror.

In reality the light doesn't reflect right a the surface. It penetrates up to a few skin depths, wherein it has all kinds of quantum mechanical interactions with the metal. That's where the macroscopic wave/particle model breaks down. Unfortunately if you truly want to understand what happens to the fields at that point, you need to do some pretty intense quantum mechanics, including modeling induced oscillations in the carrier electrons within the metallic film which coherently reradiate the incoming light.

I'm NOT one of those people who understands it. I prefer to just assume that the light hits the surface, some magic happens, then it comes back out. :p

Thanks