Ononot — Let A be a 3 \times 3 symmetric matrix with trace 9, determi

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Eigenvalues & Eigenvectorshard

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Let $A$ be a $3 \times 3$ symmetric matrix with trace $9$ , determinant $8$ , and sum of eigenvalues taken two at a time ( $\lambda_1\lambda_2 + \lambda_2\lambda_3 + \lambda_3\lambda_1$ ) equal to 26. What is the trace of $A^{-1}$ ?