What exactly is this question asking us to do? Are just supposed to just give a matrix $C$ where $AC \neq CA$?
I think Part (b) asks you to find concrete examples of matrices $B$ and $C$ such that $AB=BA$ and $AC\neq CA$. In part (a), you must have obtained a formula for $B$ so that $AB=BA$. Thus if a matrix $C$ does not satisfy the formula, then $AC\neq CA$.
So, you may randomly find a matrix $C$ such that $AC\neq CA$ but part (b) narrows down the possibility.