Could you help me with this question please?

If a is a state of a Markov chain, we say that a is 2-periodic if for all odd k.

a) Show that if i is 2-periodic and j is a element of the same communicating class as i then j is 2-periodic. (We say that 2-periodicity is a class property.)

[Hint: Assume that i is 2-periodic but j is not 2-periodic and deduce a contradiction.]

Thank you.