Every 2x2 stochastic matrix $A$ has the form $$A = \left[\begin{array}{cc} a &1-b\cr 1-a &b\cr \end{array}\right]$$
where $0\leq a\leq 1$ and $0\leq b \leq 1$.

1) True or False? Every 2×2 stochastic matrix has at least one steady-state vector.
     True    False

2) Assume $A\neq \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}$. If $A$ has a steady-state vector enter it here. If it has no steady-state matrix enter the zero vector.

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