$\begin{array}{l}\left|\begin{array}{l}\text{ 0 xyz x-z }\\ \text{y-x 0 y-z}\\ \text{z-x z - y 0}\end{array}\right| \text{is equal to}\\ \end{array}$

detailed solution

Correct option is A

We have ,  0     xyz  x-z y-x    0    y-zz-x  z - y   0=z-x   xyz  x-z z-x    0    y-zz-x  z - y   0             ∵ C1→C1- C3                              =(z-x)1   xyz  x-z 1    0    y-z1  z - y   0             taking(z-x)common from column 1                                     (Expanding along R1)                             =(z-x)[1.{-(y-z)(z-y)-xyz(z-y)+(x-z)(z-y)]=(z-x)(z-y)(-y+z-xyz+x-z)=(z-x)(z-y)(x-y-xyz)=(z-x)(y-z)(y-x+xyz)