Question

Let \(M\) be a \(2 \times 2\) matrix with the property that the sum of each of the rows and also the sum of each of the columns is the same constant \(c\). Which (if any) any of the vectors
\[
U:=\left(\begin{array}{l}
1 \\
0
\end{array}\right), \quad V:=\left(\begin{array}{l}
0 \\
1
\end{array}\right), \quad W:=\left(\begin{array}{l}
1 \\
1
\end{array}\right),
\]
must be an eigenvector of \(M ?\)