Let $f$ be an antisymmetric endomorphism of $E$. Let $g$ be an antisymmetric endomorphism of $E$, such that $fg = -gf$. Show that: $\forall x \in E, \langle f(x), g(x) \rangle = 0$.
Let $f$ be an antisymmetric endomorphism of $E$. Let $g$ be an antisymmetric endomorphism of $E$, such that $fg = -gf$. Show that: $\forall x \in E, \langle f(x), g(x) \rangle = 0$.