I want to evaluate the determinant of the $n \times n$ matrix
$\left|\begin{array}{ccccc} 1 & 0 & \ldots & 0& 0 \\ 0 & 0 & \ldots & 0 & -a\\ 0 & 0 & \ldots & -a & 0\\ &&&\vdots \\ 0 & -a & 0 &\dots & 0 \end{array}\right|.$
So I try to say that it is $(-1)^{ n + (n-1) + \ldots n-(n-2)}(-a)^{n-1}$. So power of -1 should be $\frac{(n-1)(n+2)}{2} + n-1$. However answer given is $n(n-1)/2$. Where is wrong?