Determinant of dual basis inner products $\det[(e^i,e^j)_{V^{\ast}}]$

Question

$$\det[(e^i,e^j)_{V^{\ast}}]=(-1)^{N-S}$$

Where $S$ is the signature of the metric and dimensionality of underlying vector space is $\dim V=N$. How is this equation holds/How is it derived? Does it work only for the Minkowski metric? Or this is true for any arbitrary metric?