If $a_{ij}$ represents the elements of $i^{th}$ row and $j^{th}$ column and $A_{ij}$ is the corresponding cofactor, then for the matrix $A=\begin{bmatrix} 1 & -1 & 0\\2 & 0 & 1\\3 & 4 & 2\end{bmatrix}$ the value of $a_{11}A_{21}+a_{12}A_{22}+a_{13}A_{23}$ is :

0

The correct answer is Option (2) → 0

$A=\begin{bmatrix} 1 & -1 & 0\\2 & 0 & 1\\3 & 4 & 2\end{bmatrix}$

According to property of matrix if the co-factor of one row is multiplied with the element of the other row, the result will be zero always