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    Determinant of symmetric matrix with non negative integer element

    Try n=4
  2. G

    Is the Determinant of a Symmetric Matrix with Zero Diagonal Elements Non-Zero?

    all different element
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    Determinant of symmetric matrix with non negative integer element

    Let \begin{equation*} A=% \begin{bmatrix} 0 & 1 & \cdots & n-1 & n \\ 1 & 0 & \cdots & n-2 & n-1 \\ \vdots & \vdots & \ddots & \vdots & \vdots \\ n-1 & n-2 & \cdots & 0 & 1 \\ n& n-2 & \cdots & 1 & 0% \end{bmatrix}% \end{equation*}. How can you prove that det(A)=[(-1)^n][n][2^(n-1)]? Thanks.
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    Is the Determinant of a Symmetric Matrix with Zero Diagonal Elements Non-Zero?

    How to prove that the determinant of a symmetric matrix with the main diagonal elements zero and all other elements positive is not zero and different ?
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