If \( a \neq b \neq c \) such that \( \left|\begin{array}{ccc}a^{3}-1 & b^{3}-1 & c^{3}-1 \\ a &...
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0If \( a \neq b \neq c \) such that \( \left|\begin{array}{ccc}a^{3}-1 & b^{3}-1 & c^{3}-1 \\ a & b & c \\ a^{2} & b^{2} & c^{2}\end{array}\right|=0 \) then
(a) \( a b+b c+c a=0 \)
(b) \( a+b+c=0 \)
(c) \( a b c=1 \)
(d) \( a+b+c=1 \)
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