Are you using an asterix to represent dot product, cross product, componentwise multiplication, or something else entirely?
It could be the cross product. The last product is c times a, not the other way around.
Edit: And if it is the cross product, you may find it useful to write c = -a-b.
You then need to check that b*c and c*a are both equal to a*b (recall that the cross product is linear in both variables (like any good product), and that x*x=0 for all x).