If A is 5 by 5, then AB - BA = 0 gives 25 equations for the 25 entries in B. Show that the 25 by 25 matrix is singular by noticing a simple nonzero solution B.
I'm not 100% sure exactly what you're trying to ask, but taking $\displaystyle B=I_n$, the $\displaystyle n\times n$ identity matrix, definitely satisfies your equation.
I'm not exactly sure myself. I get confused by the way the questions in this book are worded. I guess I thought it might make more sense to someone else.
Thanks for answering.