If $$D = \left| {\matrix{ 1 & 1 & 1 \cr 1 & {1 + x} & 1 \cr 1 & 1 & {1 + y} \cr } } \right|$ for $x \ne 0,y \ne 0,$ then $D$$ is :

Question

divisible by $x$ but not $y$

divisible by $y$ but not $x$

divisible by neither $x$ nor $y$

divisible by both $x$ and $y$

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