If $x,y,z$ are all different from zero and $\begin{vmatrix}1+x & 1 & 1\\1 & 1+y & 1\\1 & 1 & 1+z\end{vmatrix}$ = 0, then value of $x^{-1}+y^{-1}+z^{-1}$ is

Question

$\begin{array}{1 1} xyz \\ x^{-1}y^{-1}z^{-1} 1 \\ -x-y-z \\ -1\end{array} $