If $f(x)=\begin{vmatrix}1 &x&x+1\\2x&x(x-1)&(x+1)x\\3x(x-1)&x(x-1)(x-2)&(x+1)x(x-1)\end{vmatrix}$ then $f(100)$ is equal to

Question

$(a)\;0\qquad(b)\;1\qquad(c)\;100\qquad(d)\;-100$