Hello,

I am trying to compute the determinant of the following matrix:

$\displaystyle \begin{bmatrix}2&-2&1&0&0&0&0&0\\-2&2&-2&1&0&0&0&0\\1&-2&2&-2&1&0&0&0\\0&1&-2&2&-2&1&0&0\\0&0&1&-2&2&-2&1&0\\0&0&0&1&-2&2&-2&1\\0&0&0&0&1&-2&2&-2\\0&0&0&0&0&1&-2&2\end{bmatrix}$

What would be the fastest way to do this?

I was thinking about computing the row reduced echelon form first, which is equal to the 8 by 8 identity matrix and then compute the product of the elements on the main diagonal which equals 1. Is there a fast way to compute the row reduced echelon form of this matrix? The nice pattern in this matrix suggests that there is.

If this is not the fastest way of computing the determinant, please tell me. All suggestions are welcome. Thanks!