The value of a for which the system of equations $a^3x+(a+1)^3y+(a+2)^3z=0,ax+(a+1)y+(a+2)z=0,x+y+z=0$ has a non-zero solution is

Question

$\begin{array}{1 1}(A)\;1&(B)\;0\\(C)\;-1&(D)\;\text{None of these}\end{array}$