Let $K$ be a field.

(i) Let $F$ and $F^{\prime}$ be two finite extensions of $K$. When the degrees of these two extensions are equal, show that every $K$-homomorphism $F \rightarrow F^{\prime}$ is an isomorphism. Give an example, with justification, of two finite extensions $F$ and $F^{\prime}$ of $K$, which have the same degrees but are not isomorphic over $K$.

(ii) Let $L$ be a finite extension of $K$. Let $F$ and $F^{\prime}$ be two finite extensions of $L$. Show that if $F$ and $F^{\prime}$ are isomorphic as extensions of $L$ then they are isomorphic as extensions of $K$. Prove or disprove the converse.