Find a $3 \times 3$ stochastic matrix $A$ that has exactly one initial state vector $x_0$ that will generate a Markov chain with a steady-state vector.

$A =$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$				$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$