MCQ
If$\text{A}=\begin{vmatrix}\text{a}_{11}&\text{a}_{12}&\text{a}_{13}\\\text{a}_{21}&\text{a}_{22}&\text{a}_{23}\\\text{a}_{31}&\text{a}_{32}&\text{a}_{33}\end{vmatrix}$ and $C_{ij}$ is cofactor of $a_{ij}$ in a, then value of $|A|$ is given by:
  • A
    $a_{11}C_{31} + a_{12}C_{32} + a_{13}C_{33}$
  • B
    $a_{11}C_{11} + a_{12}C_{21} + a_{13}C_{31}$
  • C
    $a_{21}C_{11} + a_{22}C_{12} + a_{23}C_{13}$
  • $a_{11}C_{11} + a_{21}C_{21} + a_{13}C_{31}$

Answer

Correct option: D.
$a_{11}C_{11} + a_{21}C_{21} + a_{13}C_{31}$
Properties of determinants state that if a is a square matrix of the order $n,$
 then Det $(A)$ is the sum of products of elements of a row $($or a column$)$ with the
corresponding cofactor of that element.

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