$∣ ∣ ∣ ∣ \begin{matrix} 0 & 2005 & 2006 - 2005 & 0 & - 2007 - 2006 & 2007 & 0 \end{matrix} ∣ ∣ ∣ ∣$

2005

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2006

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2007

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0

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Solution

The correct option is D $0$
Let $A = ∣ ∣ ∣ ∣ \begin{matrix} 0 & 2005 & 2006 - 2005 & 0 & - 2007 - 2006 & 2007 & 0 \end{matrix} ∣ ∣ ∣ ∣$
Expanding the determinant we get,
$A = - (2005) [- (2006) (2007)] + 2006 (- (2005) (2007))$
$= 0$

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