Question
Let A be a 2 × 2 matrix
Statement 1 : adj (adj A) = A
Statement 2 : |adj A| = |A|
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Statement–1 is true, Statement–2 is true, Statement–2 is a correct explanation for statement–1
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Statement–1 is true, Statement–2 is true; Statement–2 is not a correct explanation for statement–1.
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Statement–1 is true, statement–2 is false.
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Statement–1 is false, Statement–2 is true
Solution
A.
Statement–1 is true, Statement–2 is true, Statement–2 is a correct explanation for statement–1
adj(adjA) = |A|n – 2A,
where |A| = determinant of A but n = 2
⇒ A also |adj A| = |A|n – 1
⇒ |A| Statement–1 is true and Statement–2 is also true and Statement–2 is correct explanation of Statement–1.
