I suck at these, especially in the complex field. This one's thankfully a real one but I'm having some trouble.

Let A, B be 2x2 matrices with real entries st lim A^m, lim B^m, and lim (AB)^m exist as m --> inf, but Lim (AB)^m != (lim A^m)(lim B^m). Find A & B.

I'm assuming there's no one correct answer.