Given a Markov chain with the transition probability matrix of

$\displaystyle P = \begin{bmatrix}0 & 0.6 & 0 & 0.4\\0.4 & 0 & 0.6 & 0\\0 & 0.4 & 0 & 0.6\\0.6 & 0 & 0.4 & 0\end{bmatrix}$

which of the following is false?

a) The chain is aperiodic

b) The state space of the cahin is a communicating class

c) The chain is ergodic

d) The chain is irreducible

Thanks.