NFA/DFA for $ L= \{a^n b^n a | n\ge0\}$
Since FSM's can't count identical sequences, I don't think both of your answers would be correct. You can take a look here, (pumping lemma) to prove why $L= \{a^nb^n | n \ge 0 \}$ is not regular, thus you can't write a FSM for it. Also a good example here shows the proof. On the other hand it would be different if you are meaning $a^*b^*a$ which can be written as a FSM.