Question $3(2$ pts$).$ Prove the following lemma, by using the proof by contradiction:

Lemma. If F$6=\{0,1,$ a$,$ a$2,$ a$3,$ a$4\}$ is a field, then there exists some x in $\{1,$ a$,$ a$2$ a$3$ a$4\}$ s$.$t$.$x $+$ x $=0.$

Hint You might find the previous lemma in Q$2$ usefu