1. The problem statement, all variables and given/known data A is nxn B is nxp Is the rank of [B AB ... An-1B] equal to the rank of [AB A2B ... AnB]? If not, under what condition will the ranks be equal? 3. The attempt at a solution I don't even know where to start. I know that both matrices should have the same number of pivots, but since this is so generalized I don't know how to learn anything about how multiplying by A would change the number of pivots! Can someone help me out and at least give me a hint? I've been staring at this for the longest time and just don't know what to do! Thanks!