Consider a system consisting of two electrons with Slater-Determinant $\vert\chi_1\chi_2\rangle$, where $\chi_1$ and $\chi_2$ are one-electron orbitals (spin-orbitals). The Slater Determinant is normalized, i.e, $\langle\chi_1\chi_2\vert\chi_1\chi_2\rangle=1$. Further, the antisymmetry of $\vert\chi_1\chi_2\rangle$ manifests as

$$\vert\chi_2\chi_1\rangle=-\vert\chi_1\chi_2\rangle.$$

Project now the latter relation on $\langle\chi_1\chi_2\vert$, i.e.,

$$\langle\chi_1\chi_2\vert\chi_2\chi_1\rangle=-\langle\chi_1\chi_2\vert\chi_1\chi_2\rangle=-1.$$

My Question: What does the relation $\langle\chi_1\chi_2\vert\chi_2\chi_1\rangle=-1$ mean?