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Let $M_n= \begin{bmatrix} n-1 & n-2 & n-3 & ... & 1& 0\\ n-2 & n-3 & n-4 & ... & 0& 1\\ n-3 & n-4 & n-5 & ... & 1&2\\ \vdots & \vdots & \vdots & \ddots & \vdots & \vdots\\ 1& 0 & 1 &...& n-3 & n-2\\ 0 & 1 & 2 &... & n-2&n-1 \end{bmatrix}$

What's $\det(M_n)$ ?

Can someone help me with this, I tried Using Laplace's formula and transformations of rows but it didn't work. original problem

stranger
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    Looks like a special case of https://math.stackexchange.com/questions/770117/determinant-of-circulant-matrix. – Martin R Jan 18 '19 at 22:07
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    @MartinR Not sure. In this case $a_{11}=a_1=n-1$, while $a_{n2}=1\neq a_{11}$. Nevertheless, it may be a OP's typo. We will see... – Dog_69 Jan 18 '19 at 22:42
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    @m2017m Please see MartinR's comment and check your formula. There might be a typo in you second and third columns. – Dog_69 Jan 18 '19 at 22:46
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    there is no typo, formula is good – stranger Jan 19 '19 at 11:07

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