MCQ
If $A = \left[ {\begin{array}{*{20}{c}}
{1 + {a^2} + {a^4}}&{1 + ab + {a^2}{b^2}}&{1 + ac + {a^2}{c^2}} \\
{1 + ab + {a^2}{b^2}}&{1 + {b^2} + {b^4}}&{1 + bc + {b^2}{c^2}} \\
{1 + ac + {a^2}{c^2}}&{1 + bc + {b^2}{c^2}}&{1 + {c^2} + {c^4}}
\end{array}} \right]$
{1 + {a^2} + {a^4}}&{1 + ab + {a^2}{b^2}}&{1 + ac + {a^2}{c^2}} \\
{1 + ab + {a^2}{b^2}}&{1 + {b^2} + {b^4}}&{1 + bc + {b^2}{c^2}} \\
{1 + ac + {a^2}{c^2}}&{1 + bc + {b^2}{c^2}}&{1 + {c^2} + {c^4}}
\end{array}} \right]$
and $det(A) = det(4I)$, where $I$ is $3 × 3$ identity matrix, then $(a -b)^3 + (b -c)^3 + (c -a)^3$ can be equal to -
- ✓$-24$
- B$6$
- C$-6$
- D$12$