Question

Consider the determinant, $\Delta =\left|\begin{array}{ccc}p& q& r\\ x& y& z\\ l& m& n\end{array}\right|$ $M_0$ denotes the minor of an element in $i$th row and $j$th column and $C_{ij}$ denotes the cofactor of an element in $i$th row and $j$th column.
The value of $p.C_{21}+q.C_{22}+r.C_{23}$ is equal to

• A. $0$
• B. $-\Delta$
• C. $\Delta$
• D. ${\Delta }^2$

Answer 1

The correct option is A $0$

From the property of determinants, if any element is multiplied with cofactor of corresponding element of another row, and summed up for each element of original row, the sum comes out zero $\Rightarrow \left(A\right)$