First some Definitions for convenience:
Let ${\mathfrak {g}}$ be a real semisimple Lie algebra and let $B(\cdot ,\cdot )$ be its Killing form. An involution on ${\mathfrak {g}}$ is a automorphism whose square is the identity. Such an involution is called a Cartan involution on ${\mathfrak {g}}$ if $B_{\theta }(X,Y):=-B(X,\theta Y)$ is a positive definite bilinear form.
The question:
Prove the identity map of ${\mathfrak {g}}$ is the unique Cartan involution if the Killing form is negative definite.