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Question: Answered & Verified by Expert
If $A=\left[a_{i j}\right]_{3 \times 3}=\left[\begin{array}{lll}3 & 2 & 4 \\ 1 & 4 & 1 \\ 2 & 6 & 3\end{array}\right]$ and $A_{i j}$ is a cofactor of $a_{i j}$, then the value of $a_{21} A_{21}+a_{22} A_{22}+a_{23} A_{23}$ is equal to
MathematicsDeterminantsMHT CETMHT CET 2022 (08 Aug Shift 2)
Options:
  • A 18
  • B 8
  • C -8
  • D 0
Solution:
1385 Upvotes Verified Answer
The correct answer is: 8
$a_{21} A_{21}, a_{22} A_{22}+a_{23} A_{23}=|A|=3 \times(12-6)-2(3-2)+4(6-8)=8$

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