Can someone explain how to solve this step by step? I have to find determinant(A).
subtract the first row from every other row (this won't change the determinant). this gets you:
$\displaystyle \begin{vmatrix}-8&u&\dots&u\\u+8&-8-u&\dots&0\\ \vdots&\vdots&\ddots&\vdots\\u+8&0&\dots&-8-u\end{vmatrix}$
next, add every column to the first (this also will not change the determinant) to get:
$\displaystyle \begin{vmatrix}-8-u + nu&u&\dots&u\\0&-8-u&\dots&0\\ \vdots&\vdots&\ddots&\vdots\\0&0&\dots&-8-u\end{vmatrix}$
this shouldn't be too hard to calculate.