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

Let A be a $2 \times 2$ matrix Statement-1 $: \operatorname{adj}(\operatorname{adj} A)=A$ Statement-2 : $|\operatorname{adj} \mathrm{A}|=|\mathrm{A}|$
  1. Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1
  2. Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
  3. Statement-1 is true, Statement-2 is false
  4. 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} $

Asked in: JEE Main 2009

Practice more Matrices questions on Aicharya