provide solution for RD Sharma maths class 12 chapter 5 Determinants exercise  Fill in the blanks question 18

Hint: Here, we use basic concept of determinant of matrix

Given:     $\Delta=\left[\begin{array}{ccc} 0 & x-y & y-z \\ y-x & 0 & z-x \\ z-y & x-z & 0 \end{array}\right]$

Solution: Here $\Delta$ is skew symmetric matrix.

Here, clearly we can see that $\Delta$ is skew symmetric and its diagonal are 0

So, $\Delta=0$