Question

If $D=\begin{vmatrix}a_{11} & a_{12} \\ a_{21} & a_{22}\end{vmatrix}$ and corresponding cofactors of elements be written as $c_{11}, c_{12}, c_{21}$ and $c_{22}$, then the value of $a _{11} c _{21}+ a _{12} c _{22}+ a _{21} c _{11}+ a _{22} c _{12}$ is equal to

• A. 0
• B. $D$
• C. $2 D$
• D. $- D$

Answer 1

Answer: (A)

$ \Theta a_{11} c_{21}+a_{12} c_{22}=0 $
$\text { and } a_{21} c_{11}+a_{22} c_{12}=0 $
$\therefore \text { sum }=0 $