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If `x , y , z` are different from zero and `[[1+x,1, 1],[ 1 ,1+y,1 ],[1 ,1 ,1+z]]=0` then the value of `x^(-1)+y^(-1)+2^(-1)` is `x y z` (b) `x^(-1)y^(-1)z^(-1)` (c) `-x-y-z` (d) `-1`

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Given,
`[[1+x,1, 1],[ 1 ,1+y,1 ],[1 ,1 ,1+z]]=0`
`[[x,-y, 0],[ 0 ,y,-z ],[1 ,1 ,1+z]]=0`
use `R_1​->R_1​−R_2`​ and `R_2​->R_2​−R_3​`
Now expand along first row,
`⇒x[y(1+z)+z]+y(0+z)=0`
...
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