$\displaystyle

\left(

\begin

{array}

{ccccc}

1&n&n&...&n\\

n&2&n&...&n\\

n&n&3&...&n\\

...&...&...&...&...\\

n&n&n&...&n

\end

{array}

\right)

$

The solution is $\displaystyle (-1)^{(n-1)}*n! $

Would someone be so kind and explain me how to do it? Thanks in advance!