markov process and classification of states

a)classify each of the states for the following markov chain (ie transient, recurent absorbing) and state how many classes there are

0.3 0.7 0

0.3 0 0.7

1 0 0

i have that each state is recurent and there is a single recurent class.

b)show that this markov chain is aperiodic without computing P^n (ie use the fact that if we can transition to a state in integer values>1 then the chain has no specific period.

i am still trying to make sense of the periodicity concept. Does it mean that we can get back to a certain state, having started there after transitioning to all other possible states in only certain integer valus or multiples of this. Or does it mean that we can get back to a certain state having started there in any number of steps, but it is not actually necassary to transition through all possible states.