question_answer

If\[\left| \begin{matrix}    a & {{a}^{2}} & 1+{{a}^{3}}  \\    b & {{b}^{2}} & 1+{{b}^{3}}  \\    c & {{c}^{2}} & 1+{{c}^{3}}  \\ \end{matrix} \right|=0\]and vectors\[(1,a,{{a}^{2}}),\]\[(1,b,{{b}^{2}})\] and \[(1,c,{{c}^{2}})\] are non-coplanar, then the product abc equals

A)  \[0\]                            

B) \[-1\]

C)  \[1\]                            

D)  \[2\]

E)  None of these