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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 $M ?$
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