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 xin$\{1,a,a^2,a^3,a^4\}$ s$.$t$.$

$x+x=0.$

Hint You might find the previous lemma in $Q2$ useful.