If x y z are all different and not equal to zero and \(\left| {\begin{array}{*{20}{c}} {1 + x}&1&1\\ 1&{1 + y}&1\\ 1&1&{1 + z} \end{array}} \right| = 0\) then the value of x-1 + y-1 + z-1 is equal to

1
-1
2
- x - y - z
3
 x-1y-1z-1
4
xyz

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