Let A be a 2 × 2 matrix.
Statement-1: $adj (adj\, A) = A$
Statement-2: $|adj\, A|=|A|$
Answer & explanation
Correct answer: option 2
For any square matrix A of order n, we have
$|adj\, A|=|A|^{n-1}$ and $adj (adj\, A) =|A|^{n-2} A$
For a 2 × 2 matrix, we have n = 2.
$|adj\, A|=|A|$ and $adj (adj\, A) = A$
Also, $adj (adj\, A) =|A|^{n-2} A$ is obtained by replacing A by $adj\, A$ in the relation $A (adj\, A) =|A|I_n$
Hence, both the statements are true. But, statement-2 is the correct explanation for statement-1.