Let $A\left( {\begin{array}{*{20}{c}} {{x_1}} & 0 \\ 0 & {{x_2}} \\ \end{array}} \right)\left( {\begin{array}{*{20}{c}} 1 \\ 1 \\ \end{array}} \right) = \lambda \left( {\begin{array}{*{20}{c}} {{x_1}} \\ {{x_2}} \\ \end{array}} \right)$
where $A \in {M_2}(R)$ and all $a_{ij}\ge 0$, and for some $x_1\ge 0$ ,$x_2 \ge 0$.
Can we say that $ A$ is diagonally similar to a matrix, all of whose row sums are equal?