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Let A be 2 x 2 matrix.Statement I adj (...

Let A be 2 x 2 matrix.Statement I `adj (adj A) = A` Statement II `|adj A| = A`

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 a correct explanation for statement 1.

C

Statement 1 is true, statement 2 is false.

D

Statement 1 is false, statement 2 is true.

Text Solution

Verified by Experts

The correct Answer is:
B
`|"adj A"|=|A|^(n-1)=|A|^(2-1)=|A|`
adj (adj A)`=|A|^(n-2) A=|A|^(0) A=A`
Thus both statements are true, but statement 2 is not correct explanation of statement 1.
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Knowledge Check

  • Let A be a 2xx2 matrix. Statement 1: adj(adjA)=A Statement 2: |adjA|=|A| .

    A
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