Question

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

• A. 110
• B. 22
• C. -110
• D. -22

Answer 1

Answer: (A)

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