# How to find determinant of the matrix $N\times N$

How to find determinant of the matrix NxN? $$\left| \begin{array}{ccccc} a^{n} & (a - 1)^{n} & \cdots & (a-n)^{n} \\ a^{n - 1} & (a - 1)^{n - 1} & \cdots & (a-n)^{n - 1} \\ \cdots & \cdots & \cdots & \cdots \\ a & a - 1 & \cdots & a-n\\ 1 & 1 & \cdots & 1 \end{array} \right|$$

• That appears to be a $(n+1) \times (n+1)$ matrix... – aras Dec 20 '15 at 12:30
• There is N = (n + 1) – user3513483 Dec 20 '15 at 12:44
• Hint: look up the formula for determinants of Vandermonde matrices. – HSN Dec 20 '15 at 12:47