If x, y, z are different from zero and |(1+x, 1, 1)(1, 1+y, 1)(1, 1, 1+z)| = 0,

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

A. xyz

B. x-1y-1z-1

C. - x - y - z

D. –1

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Correct answer is D.

x[(1 + y)z + y] -1[- yz] = 0

xz + xyz+ xy + yz = 0 (divide by xyz in both side)