If the system of equations \[ \begin{array}{ll} a x+a y-z & =0 \\ b...

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If the system of equations
\[
\begin{array}{ll}
a x+a y-z & =0 \\
b x-y+b z & =0 \\
-x+c y+c z & =0
\end{array}
\]
(where \( a, b, c \neq-1 \) ) has a non-trivial solution, then value of
\( -\frac{1}{1+a}+\frac{1}{1+b}+\frac{1}{1+c} \) is
(a) 2
(b) \( -1 \)
(c) \( -2 \)
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