Answer
$P_{B \leftarrow C}=\begin{bmatrix}
\frac{1}{7} & -\frac{2}{7} \\
-\frac{2}{7} & \frac{3}{7}
\end{bmatrix}$
Work Step by Step
From problem 20 we have $P_{C \leftarrow B} =\begin{bmatrix}
3 & -2\\
2 & 1\\
\end{bmatrix}$
Since $P_{B \leftarrow C}=(P_{C \leftarrow B})^{-1}$ we have $P_{B \leftarrow C}=\begin{bmatrix}
\frac{1}{7} & -\frac{2}{7} \\
-\frac{2}{7} & \frac{3}{7}
\end{bmatrix}$
