If the system of equations $ax+y+z=0$, $x+by+z=0$, $x+y+cz=0$, where $(a,b,c\neq 1)$ has a non-trivial solutions, then the value of $\large\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}$ is

Question

$(a)\;-1\qquad(b)\;0\qquad(c)\;1\qquad(d)\;None\;of\;these$