A problem on mutlilinear algebra

Question

In Greub's book on multilinear algebra, a problem asked to show $B(E,F;G)$ is isomorphic to $L(E;L(F;G))$ where $B(E,F;G)$ denotes the bilinear mapping from $E*F$ to $G$ and $L(A;B)$ denotes linear mapping from $A$ to $B$. $E$, $F$ and $G$ are vector spaces. Can I have some hints on how to prove it rather than someone gave me a full proof?

Answer 1

Hint: $B(E,F;\,G)$ contains maps of the form $\langle e,f\rangle\ \mapsto\ g$ and $L(E;\,L(F;G))$ contains maps of the form $e\mapsto\,(f\mapsto g)$, where obviously I meant $e\in E,\ f\in F,\ g\in G$.