Evaluate the determinant
$\begin{vmatrix} x-y & y-z & z-x\\y-z& z-x & x-y \\z-x & x-y & y-z \end{vmatrix}$
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 0
$\begin{vmatrix} x-y & y-z & z-x\\y-z& z-x & x-y \\z-x & x-y & y-z \end{vmatrix}$
$R_1→R_1+R_2+R_3$
$=\begin{vmatrix} 0 &0 & 0\\y-z& z-x & x-y \\z-x & x-y & y-z \end{vmatrix}=0$