If $A=\begin{bmatrix}152&105&3\\149&25&35\\2&1&0\end{bmatrix}$. If $A_{ij}$ denotes the co-factor of an element $a_{ij}$ of the matrix A, then the value of $a_{11}A_{21} + a_{12}A_{22} + a_{13}A_{23}$ is equal to

0

The correct answer is Option (2) → 0

Given:

$A=\begin{bmatrix}152 & 105 & 3\\149 & 25 & 35\\2 & 1 & 0\end{bmatrix}$

Required expression: $a_{11}A_{21}+a_{12}A_{22}+a_{13}A_{23}$.

By determinant property, $\displaystyle \sum_{k=1}^{n}a_{1k}A_{2k}=0$ because elements and cofactors from different rows yield zero.

$a_{11}A_{21}+a_{12}A_{22}+a_{13}A_{23}=0$