Find a matrix $B$ such that $ABA=A$ and $BAB=B$, where $A=\left[\begin{array}{ccc} -3 &3 &3\cr 1 &5 &11\cr -3 &0 &-3 \end{array}\right]$.
$B =$ $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$