##### Exercise7

Using the results of the previous exercise, we would like to explain why $$A^2$$ is a stochastic matrix if $$A$$ is stochastic.

1. Suppose that $$A$$ and $$B$$ are stochastic matrices. Explain why the product $$AB$$ is a stochastic matrix by considering the product $$SAB\text{.}$$

2. Explain why $$A^2$$ is a stochastic matrix.

3. How do the steady-state vectors of $$A^2$$ compare to the steady-state vectors of $$A\text{?}$$

in-context