The value of the determinant

$D=\begin{vmatrix} x & a & a+x\\y & b & b+y \\z & c & c+z\end{vmatrix}$ is :

0

The correct answer is Option (1) → 0

$D=\begin{vmatrix} x & a & a+x\\y & b & b+y \\z & c & c+z\end{vmatrix}$

$=\begin{vmatrix} x & a & a\\y & b & b\\z & c & c\end{vmatrix}+\begin{vmatrix} x & a & x\\y & b & y \\z & c & z\end{vmatrix}$

$=0+0$

$=0$