Let \begin{equation*}(adsbygoogle = window.adsbygoogle || []).push({});

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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# Determinant of symmetric matrix with non negative integer element

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