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JEE Main & Advanced AIEEE Solved Paper-2009

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    Directions: Questions No. 89 are Assertion - Reason type questions. Each of these questions contains two statements: Statement-1 (Assertion) and Statement-2 (Reason). Each of these questions also have four alternative choices, only one of which is the correct answer. You have to select the correct choice. Let A be a 2 × 2 matrix Statement 1: adj (adj A) = A Statement 2:\[|adj\text{ }A|=|A|\]     AIEEE  Solved  Paper-2009

    A) Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for statement-1

    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

    Correct Answer: A

    Solution :

    \[adj(adjA)=|A{{|}^{n2}}A,\]where\[|A|=\]determinant of A but\[n=2\] \[\Rightarrow \]A also \[|adjA|=|A{{|}^{n-1}}\Rightarrow |A|\] Statement-1 is true and Statement-2 is also true and Statement-2 is correct explanation of Statement-1.


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