If A - begin vmatrix 1 - 1 - 11 -a - b - c 1a- b- 3 - c- 3end vmatrix - B - -begin vmatrix 1 - 1 - 111a - 2 - b - 2 - c - 2 1a- 3 - b- 3 - c- 3lend vmatrix - C - -begin vmatrix a - b - ca- 2 - b- 2 - c- 2 la- b- 3 - c- 3lend vmatrix - then which relation is correctA- A - CB- B-CC- A - BD- None of these

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Properties of Determinants

If A = begin ...

Question

If $A = ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 a & b & c a^{3} & b^{3} & c^{3} \end{matrix} ∣ ∣ ∣ ∣, B = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 a^{2} & b^{2} & c^{2} a^{3} & b^{3} & c^{3} \end{matrix} ∣ ∣ ∣ ∣ ∣, C = ∣ ∣ ∣ ∣ ∣ \begin{matrix} a & b & c a^{2} & b^{2} & c^{2} a^{3} & b^{3} & c^{3} \end{matrix} ∣ ∣ ∣ ∣ ∣,$ then which relation is correct

A = B

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A = C

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B = C

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None of these

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A = ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 a & b & c a^{3} & b^{3} & c^{3} \end{matrix} ∣ ∣ ∣ ∣, B = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 a^{2} & b^{2} & c^{2} a^{3} & b^{3} & c^{3} \end{matrix} ∣ ∣ ∣ ∣ ∣, C = ∣ ∣ ∣ ∣ ∣ \begin{matrix} a & b & c a^{2} & b^{2} & c^{2} a^{3} & b^{3} & c^{3} \end{matrix} ∣ ∣ ∣ ∣ ∣,

∣ ∣ ∣ ∣ ∣ \begin{matrix} b c & a & a^{2} c a & b & b^{2} a b & c & c^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣ = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & a^{2} & a^{3} 1 & b^{2} & b^{3} 1 & c^{2} & c^{3} \end{matrix} ∣ ∣ ∣ ∣ ∣

∣ ∣ ∣ ∣ ∣ \begin{matrix} a & a^{2} & b c b & b^{2} & c a c & c^{2} & a b \end{matrix} ∣ ∣ ∣ ∣ ∣ = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & a^{2} & a^{3} 1 & b^{2} & b^{3} 1 & c^{2} & c^{3} \end{matrix} ∣ ∣ ∣ ∣ ∣

∣ ∣ ∣ ∣ ∣ \begin{matrix} a & a^{2} & b c b & b^{2} & c a c & c^{2} & a b \end{matrix} ∣ ∣ ∣ ∣ ∣ = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & a^{2} & a^{3} 1 & b^{2} & b^{3} 1 & c^{2} & c^{3} \end{matrix} ∣ ∣ ∣ ∣ ∣

∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 a & b & c a^{3} & b^{3} & c^{3} \end{matrix} ∣ ∣ ∣ ∣ = (a - b) (b - c) (c - a) (a + b + c)

∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 (x - a)^{2} & (x - b)^{2} & (x - c)^{2} (x - b) (x - c) & (x - c) (x - a) & (x - a) (x - b) \end{matrix} ∣ ∣ ∣ ∣ ∣

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