I was just trying out some problems, when i couldn't solve this question:
- Does there exist $n \times n$ matrices $A$ and $B$ with real entries such that $ \Bigl(I - (AB-BA)\Bigr)^{n}=0?$
I really don't know how to proceed for this question. What i did was to find some examples, but that didn't quite work. Any ideas on how one goes about thinking on such problems and how to solve them would be of great help.