Exercise 2, § 8

Take $\mathfrak{g}=\mathfrak{s}\mathfrak{l}(3, k)$. Show that $x \rightarrow$ det($x$) is an invariant polynomial function on $\mathfrak{g}$ that is not invariant under Aut($\mathfrak{g}$) (use the automorphism $x \rightarrow -^tx$).