If $a,b,c$ are in A.P with common difference d and $\begin{vmatrix}x+1&x+a&x+b\\x+a&x+b&x+c\\x-b+1&x-1&x-a+c\end{vmatrix}$ has absolute value 2 then d is

Question

$\begin{array}{1 1}(A)\;a&(B)\;-2\\(C)\;\pm 1&(D)\;\text{None of these}\end{array}$