Definition of normal extension: an algebraic extension $K$ of $F$ is normal extension if every irreducible polynomial in $F[x]$ that has one root in $K$ actually splits in $K[x]$.
Let $K$ be a normal extension of the field $F$ of finite degree.Let $E$ be a subfield of $K$ containing $F$. Prove that $E$ is a normal extension of $F$ if and only if every $F$-isomorphism of $E$ onto $K$ is an $F$-automorphism of $E$?