Question

If $c_{ij}$ is the cofactor of the element $a_{ij}$ of the determinant $\begin{vmatrix}2&-3&5\\ 6&0&4\\ 1&5&-7\end{vmatrix}$, then write the value of $a_{32} \cdot c_{32}$

• A. 110
• B. 22
• C. -110
• D. -22

Answer 1

Answer: (A)

Let $A=\begin{vmatrix}2&-3&5\\ 6&0&4\\ 1&5&-7\end{vmatrix} $
Here, $a_{32}=5 $ then,
$c_{32}=\left(-1\right)^{3+2} \begin{vmatrix}2&5\\ 6&4\end{vmatrix}$
$=\left(-1\right)^{5}\left(8-30\right)=-\left(-22\right)=22$
$\therefore a_{32}. c_{32}=5 \times22=110$