Find two matrices A and B such that satisfy, A^2=0, AC +CA=1 and B=CA: where C = complex conjugate of A.?

Hhhhmmmm, a difficult question. I believe the Quadratic Formula would be the best bet for this equation. I would also do 30 jumping jacks and 40 laps in a pool. Maybe even a run down to Shave-On Drugs (The Best Place to Buy Your Rugs). I believe this would do the trick. Oh and uh by the way. Suck it.