Evaluate the Determinants A? Evaluate the  Determinants 

$$A=\left(\begin{matrix} 
  1 & 1 & 0 & 0 & 0\\
  -1 & 1 & 1 & 0 & 0\\
  0 & -1& 1 & 1 & 0\\
  0& 0 & -1 & 1 & 1\\
  0 & 0 & 0 & -1 & 1\\
\end{matrix}\right)$$

My attempst :    I  was  thinking abouts the 
Schur complement https://en.wikipedia.org/wiki/Schur_complement
$\det \begin{pmatrix}
A&B\\
C&D
\end{pmatrix}= \det (A-BD^{-1}C)\det D
$
As i  not getting  How  to applied  this  formula  and finding the Determinant of the Given question,,
Pliz help me  or is  There another  way  to find  the  determinant of the matrix.
Thanks u 

After adding the first line to the second one, your matrix becomes$$\begin{pmatrix}1 & 1 & 0 & 0 & 0\\  0 & 2 & 1 & 0 & 0\\  0 & -1& 1 & 1 & 0\\  0& 0 & -1 & 1 & 1\\  0 & 0 & 0 & -1 & 1\end{pmatrix}$$and therefore$$\det A=\begin{vmatrix}2 & 1 & 0 & 0\\ -1& 1 & 1 & 0\\ 0 & -1 & 1 & 1\\ 0 & 0 & -1 & 1\end{vmatrix}=2\begin{vmatrix}1 & \frac12 & 0 & 0\\ -1& 1 & 1 & 0\\ 0 & -1 & 1 & 1\\ 0 & 0 & -1 & 1\end{vmatrix}.$$Can you take it from here?
