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Consider the matrix \(\mathbf{C} = \begin{pmatrix} 3 & 2 \\ 3 & -2 \end{pmatrix}\).
Find the diagonal matrix \(\mathbf{D}\), the matrix \(\mathbf{P}\) and its inverse \(\mathbf{P}^{-1}\) such that \(\mathbf{C} = \mathbf{P}\mathbf{D}\mathbf{P}^{-1}\).
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