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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 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.

Text Solution

Verified by Experts

The correct Answer is:
B
For any square matrix a of order n, we have
`abs(adjA)=absA^(n-1)and adj(adjA)=absA^(n-2)A`
`:. " For a " 2xx2` matrix, we have n=2
`abs(adj A)=absAand adj(adjA)=A`
Also, `adj(adjA)=absA^(n-2)` A is obtained by replacing A by adj A in the relation `A (adjA)=absAI_n`
Hence, both the statements are true. But, statement -2 is not the correct explanation for statement - 1.
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