Answer
$P_{B \leftarrow C}=\begin{bmatrix}
0 & 0 & 0 & 1\\
1 & 0 & 0 & 0\\
0 & 0 & 1 & 0 \\
0 & 1 & 0 & 0
\end{bmatrix}$
Work Step by Step
From problem 26 we have $P_{C \leftarrow B} =\begin{bmatrix}
0 & 1 & 0 & 0\\
0 & 0 & 0 & 1\\
0 & 0 & 1 & 0 \\
1 & 0 & 0 & 0
\end{bmatrix}$
Since $P_{B \leftarrow C}=(P_{C \leftarrow B})^{-1}$ we have $P_{B \leftarrow C}=\begin{bmatrix}
0 & 0 & 0 & 1\\
1 & 0 & 0 & 0\\
0 & 0 & 1 & 0 \\
0 & 1 & 0 & 0
\end{bmatrix}$
