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For a 2 × 2 matrix A, consider the following statements: Statement I: adj(adj A) = A Statement II: |adj A| = |A| Which of the following is correct?

1. Statement I is true, Statement II is true, and Statement II correctly explains Statement I.
2. Statement I is true, Statement II is false.
3. Statement I is false, Statement II is true.
4. Statement I is true, Statement II is true, but Statement II does not correctly explain Statement I.

Correct answer: Statement I is true, Statement II is true, but Statement II does not correctly explain Statement I.

Solution

For order n=2: adj(adj A)=|A|^(n-2) A = A, so I is true; and |adj A|=|A|^(n-1)=|A|, so II is true. But II does not explain I, so the correct choice is 'both true, II not a correct explanation'.

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