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Let $A$ be an invertible matrix with eigenvalues $\lambda_{1}, \lambda_{2}, \ldots, \lambda_{k}$ and corresponding eigenvectors $\vec{v}_{1}, \vec{v}_{2}, \ldots, \vec{v}_{k}$. What can you say about the eigenvalues and eigenvectors of $A^{-1} ?$ Justify your response.
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