9.10. Suppose that L is a Lie algebra over C and that / is a symmetric, associative bilinear form of L. Show that / induces a linear map 0 : L- L*, 0(1) = B(x, -), where by B(I, -) we mean the map y -> B(x, y). Viewing both L and L as L-modules, show that 0 is an L-module homomorphism. (The L-module structure of L is given by Exercise 7.12.) Deduce that if B is non-degenerate, then L and L* are isomorphic as L-modules