Prove that the eigenvalues of a matrix are preserved under a similarity transformation; that is, if (mathbf{S}^{-1}

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Prove that the eigenvalues of a matrix are preserved under a similarity transformation; that is, if \(\mathbf{S}^{-1} \mathbf{A S}=\mathbf{B}\), then the eigenvalues of \(\mathbf{A}\) and \(\mathbf{B}\) are the same.

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