If $a,b,c$ are different and $\left| {\,\begin{array}{*{20}{c}}a&{{a^2}}&{{a^3} - 1}\\b&{{b^2}}&{{b^3} - 1}\\c&{{c^2}}&{{c^3} - 1}\end{array}\,} \right| = 0$, then

  • A

    $a + b + c = 0$

  • B

    $abc = 1$

  • C

    $a + b + c = 1$

  • D

    $ab + bc + ca = 0$

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  • [JEE MAIN 2020]