Q60 / 90 · JEE Main 2009 · Mathematics

Let A be a $2 \times 2$ matrix Statement-1 $: \operatorname{adj}(\operatorname{adj} A)=A$ Statement-2 : $|\operatorname{adj} \mathrm{A}|=|\mathrm{A}|$

  • A
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1
  • Correct answer
    B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
  • C
    Statement-1 is true, Statement-2 is false
  • D
    Statement-1 is false, Statement-2 is true

Solution

$$ \begin{aligned} & |\operatorname{adj} A|=|A|^{n-1}=|A|^{2-1}=|A| \\ & \operatorname{adj}(\operatorname{adj} A)=|A|^{n-2} A=|A|^0 A=A \end{aligned} $$

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

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