If a,b,c are non - zero real numbers and if the system of equations $\;(a-1)x =y+z\;,(b-1)y=(z+x)\;,(c-1)z=x-y\;$ , has a non - trivial solution , then ab+bc+ca equals :

Question

$(a)\;a+b+c\qquad(b)\;abc\qquad(c)\;1\qquad(d)\;-1$