How to find the determinant of this matrix I have the following matrix:
$
\begin{bmatrix}
 a & 1 & 1 & 1 \\
 1 & a & 1 & 1 \\
 1 & 1 & a & 1 \\
 1 & 1 & 1 & a \\
\end{bmatrix}
$
My approach is to rref the matrix so that i can find the determinant by multiplying along the diagonals.
I attempted to do an rref and ended up with 
$
\begin{bmatrix}
 1 & a & 1 & 1 \\
 1-a & a-1 & 0 & 0 \\
 0 & 1-a & a-1 & 1 \\
 0 & 0 & 1-a & a-1 \\
\end{bmatrix}
$
I then factored out (1-a) to get this
$
\begin{bmatrix}
 1 & a & 1 & 1 \\
 1 & -1 & 0 & 0 \\
 0 & 1 & -1 & 1 \\
 0 & 0 & 1 & -1 \\
\end{bmatrix}
$
which will then make my determinant a multipile of $(1-a)^3$: 
$\det(A) = (1-a)^3x$
But now here I don't know what to do. I have a feeling that my approach is wrong. Any help or guide please?

at lin3 col 4 is 0 not 1

det$\begin{bmatrix}
 1 & a & 1 & 1 \\
 1 & -1 & 0 & 0 \\
 0 & 1 & -1 & 0 \\
 0 & 0 & 1 & -1 \\
\end{bmatrix}$
~det$\begin{bmatrix}
 a+3 & a & 1 & 1 \\
 0 & -1 & 0 & 0 \\
 0 & 1 & -1 & 0 \\
 0 & 0 & 1 & -1 \\
\end{bmatrix}$
etc.
