If \( a, b, c \) are non-zero real numbers and if the equations \( (a-1) x=y+z,(b-1) y=z+x,(c-1)...

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If \( a, b, c \) are non-zero real numbers and if the equations \( (a-1) x=y+z,(b-1) y=z+x,(c-1) z=x+y \) has nontrivial solution, then \( a b+b c+c a \) is equal to
(A) \( a+b+c \)
(B) 1
(C) \( a b c \)
(D) none of these
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