Answer
$B=P^{-1}AP$
Work Step by Step
Multiply both sides with
$P^{-1}$ from the left, and with
$P$ from the right
$\begin{array}{crclccc}
\cdot P^{-1}/ & A & = & PBP^{-1} & /\cdot P\\
& P^{-1}AP & = & (P^{-1}P)B(P^{-1}P) & \\
& P^{-1}AP & = & (I)B(I) & \\
& P^{-1}AP & = & B &
\end{array}$
