1. The problem statement, all variables and given/known data Let A be any real 2x2 matrix. If A^m=0, prove that A^2=0. 2. Relevant equations 3. The attempt at a solution It might be quite easy, but I cannot find any way to prove it....all my attempts failed to get any closer to the solution...(I'm not sure why it is the A^2 which should equals to 0, not A^1,or A^3...) Any hint will be greatly appreciated!