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Consider the  $5\times 5$ matrix below :

$\begin{bmatrix} 1&0 &0 &0 &1 \\ 0& 1 & 1 & 1 & 0\\ 0& 1 &1 &1 &0 \\ 0& 1 &1 &1 &0 \\ 1 & 0 & 0 & 0 & 1 \end{bmatrix}$

The product of the non-zero eigenvalues of the matrix is _____.
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Bikram asked May 14, 2017
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The sum of the diagonal elements of a $ 2\times 2 $ upper triangular matrix is $-6.$ Then, the maximum possible value of the determinant of the matrix is ________.