If the system of equations $ax + y + z = 0 , x + by + z = 0 \, \& \, x + y + cz = 0$ $(a, b, c \ne 1)$ has a non-trivial solution, then the value of $\frac{1}{{1\, - \,a}}\,\, + \,\,\frac{1}{{1\, - \,b}}\,\, + \,\,\frac{1}{{1\, - \,c}}$ is :
If the system of equations $ax + y + z = 0 , x + by + z = 0 \, \& \, x + y + cz = 0$ $(a, b, c \ne 1)$ has a non-trivial solution, then the value of $\frac{1}{{1\, - \,a}}\,\, + \,\,\frac{1}{{1\, - \,b}}\,\, + \,\,\frac{1}{{1\, - \,c}}$ is :
- A
$-1$
- B
$0$
- C
$1$
- D
none of these
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