Markov Chains

I have this question and I don't understand what d) and e) are asking me and why it is a Markov Matrix.

5. Let

xn+1 = Axn be a discrete dynamical system, with the initial state x0 =
0
1

and

A =

1 0

.5
0 0.5

.

(a) Why is

A a Markov matrix?
(d) Write the initial state x0 as a linear combination of the eigenvectors of A

(with the equilibrium written as in c)).

(e) Write the solution xn by calculating xn = Anx0.