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$.x+x=0.$

Question $4(2$ pts$).$ Prove the following lemma.

Lemma. If $F_6=\{0,1,a,a^2,a^3,a^4\}$ is a field, then for any yin$\{1,a,a^2,a^3,a^4\},y+y=0.$