<s>[INST] Let \(X\) be a finite set, and let \(\psi: X \times X \to \mathbb{C}\) be a complex valued function. Let \([n]\) denote the set \(\{1, 2, \ldots, n\}\), where \(n = |X|\). Define the \(n \times n\) matrix \(M[\psi]\) whose entries are determined by \(\psi\): \[M[\psi]_{ij} = \psi(x_i, x_j).\] Show that for any permutation \(\sigma \in S_n\), the matrix \(M[\psi]^\sigma\) is equal to \(P(\sigma)M[\psi]P(\sigma)^{-1}\), where \(P(\sigma)\) is the permutation matrix corresponding to \(\sigma\).[/INST]