Q79 / 150 · MHT CET 2020 (14 Oct Shift 1) · Mathematics

If $A=\left[\begin{array}{ccc}1 & 0 & 2 \\ 2 & 1 & 3 \\ 0 & 3 & -5\end{array}\right]$, where $A_{\text {ij }}$ is the cofactor of the element $a_{\text {ij }}$ of matrix $A$, then $a_{21} A_{21}+a_{22} A_{22}+a_{23} A_{23}=$

  • A
    $-26$
  • B
    0
  • Correct answer
    C
    $-2$
  • D
    26

Solution

$\begin{aligned} a_{21} & A_{21}+a_{22} A_{22}+a_{23} A_{23} \\ &=-2(0-6)+1(-5-0)-3(3-0) \\ &=12-5-9=-2 \end{aligned}$

Hence, the correct answer is option: 'C'.

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