Solution SD.T17 Robert Beezer

The nonsingular (invertible) matrix $B$ will provide the desired similarity transformation, \begin{align*} \inverse{B}\left(BA\right)B &=\left(\inverse{B}B\right)\left(AB\right)&&\knowl{./knowls/theorem.MMA.knowl}{\text{Theorem MMA}}\\ &=I_nAB&&\knowl{./knowls/definition.MI.knowl}{\text{Definition MI}}\\ &=AB&&\knowl{./knowls/theorem.MMIM.knowl}{\text{Theorem MMIM}}\\ \end{align*}