Show psi changes sign when you exchange rows or exchange

Wave functions can be written in determinant form, a common practice in chemistry. Consider the following wave function psi = |psiA(1), psiA(2); psiB(1), psiB(2)|. Where A and B are spatial orbitals and 1 and 2 are electron labels.a) Show psi changes sign when you exchange rows or exchange columns.b) Normalize psi assuming the orbitals in the determinant are orthonormal.c) Determine the allowable spin functions for psi. Do these change when the rows or columns are switched? Why or why not.

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