If $a , b , c$ are non-zero real numbers and if the system of equations $$( a - 1 ) x = y + z$$ $$( b - 1 ) y = x + z$$ $$( c - 1 ) z = x + y$$ has a non-trivial solution, then $ab + bc + ca$ equals: (1) $-1$ (2) $a + b + c$ (3) $abc$ (4) 1
If $a , b , c$ are non-zero real numbers and if the system of equations
$$( a - 1 ) x = y + z$$
$$( b - 1 ) y = x + z$$
$$( c - 1 ) z = x + y$$
has a non-trivial solution, then $ab + bc + ca$ equals:\\
(1) $-1$\\
(2) $a + b + c$\\
(3) $abc$\\
(4) 1