\[B = 
\begin{bmatrix} 
 1  \\ 
 -1
\end{bmatrix}, \qquad 
\begin{bmatrix} 
 2  \\ 
 2
\end{bmatrix}, \qquad \]
\[C = 
\begin{bmatrix} 
 -1  \\ 
 1
\end{bmatrix}, \qquad 
\begin{bmatrix} 
 2  \\ 
 2
\end{bmatrix}, \qquad .\]

\begin{solution}
Solution:
\[\underset{C \leftarrow B}{P} =
\begin{bmatrix} 
-1 & 0   \\ 
0 & 1
\end{bmatrix}
\]
\end{solution}