Statement-1: If A is a non-singular square matrix of order n, then $|adj\, A|=|A|^{n-1}$

Statement-2: For any square matrix A of order n, $A (adj\, A) =|A| I$ and $|kA|=k|A|$

Statement-1 is True, Statement-2 is False. 

We know that

$A(adj\, A) =|A| I$

$∴|A (adj\, A)| = ||A|I|=| A|^n |A|$  $[∵ |kA|=k^n |A|]$

$⇒|A||adj\, A|=|A|^n$

$⇒|adj\, A|=|A|^{n-1}$

So, statement-1 is true. But, statement-2 is false. Because, $|kA|=k^n |A|$.