The probability of moving from one state to another lies on the interval [0 ; 1].
The only way for r12 + r21 = 2, is if r12 = r21 = 1.
(Draw this markov chain to see that there is only one possible transition path from each state.)
This implies independence since the probability of moving to state 1 from state 2, is independent of the transition history. It does not matter on the earlier states since there is only possible transition path from state 2 to state 1 - i.e. this transition will happen with probability 1.
Likewise for moving to state 2 from state 1.