Answer
$P_{B \leftarrow C}=\begin{bmatrix}
-\frac{5}{4} & -\frac{1}{4}\\
-\frac{1}{16} & -\frac{1}{16}
\end{bmatrix}$
Work Step by Step
From problem 18 we have $P_{C \leftarrow B} =\begin{bmatrix}
-1 & 4\\
1 & -20
\end{bmatrix}$
Since $P_{B \leftarrow C}=(P_{C \leftarrow B})^{-1}$ we have $P_{B \leftarrow C}=\begin{bmatrix}
-\frac{5}{4} & -\frac{1}{4}\\
-\frac{1}{16} & -\frac{1}{16}
\end{bmatrix}$