How to compute determinant of $n$ dimensional matrix? I have this example:
$$\left|\begin{matrix}
-1 & 2 & 2 & \cdots & 2\\
2 & -1 & 2 & \cdots & 2\\
\vdots & \vdots & \ddots & \ddots & \vdots\\
2 & 2 & 2 & \cdots & -1\end{matrix}\right|$$
When first row is multiplied by $2$ and added to second, to $nth$ row, determinant is:
$$\left|\begin{matrix}
-1 & 2 & 2 & \cdots & 2\\
0 & 3 & 6 & \cdots & 6\\
\vdots & \vdots & \ddots & \ddots & \vdots\\
0 & 6 & 6 & \cdots & 3\end{matrix}\right|$$
Now using laplace expansion on first column:
$$-\left|\begin{matrix}
3 & 6 &  \cdots & 6\\
\vdots & \vdots & \ddots & \vdots \\
6 & 6 &  \cdots & 3\end{matrix}\right|$$
Is it possible to get recursive relation?
What to do next?
Thanks for replies.

You can row reduce the matrix to an upper triangular matrix then take the product of all the elements of the diagonal.
