Question

Let $\left\{D_{1}, D_{2}, D_{3} \ldots D_{n}\right\}$ be the set of third order determinants that can be made with the distinct non-zero real numbers $a_{1}, a_{2}, \ldots, a_{9}$, then

• A. $\displaystyle\sum_{i=1}^{n} D_{i}=1$
• B. $\displaystyle\sum_{i=1}^{n} D_{i}=0$
• C. $D i=D_{i}, \forall_{i}, j$
• D. None of these

Answer 1

Answer: (B)

Total number of third order determinants is $9 !$
As the number of determinants are even and in which there are $\frac{9 !}{2}$ pairs of determinants which are obtained by changing two consecutive rows
So, $\displaystyle\sum_{i=1}^{n} D_{i}=0$