Let A be a 2 × 2 matrix.

Statement-1: $adj (adj\, A) = A$

Statement-2: $|adj\, A|=|A|$

Statement-1 is True, Statement-2 is True; Statement-2 is not a correct explanation for Statement-1. 

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.