$A^{-1} = \frac{adj(A)}{|A|}$
$|A| \cdot A^{-1} = adj(A)$
Multiplying by $A$ (from right) on both sides, we get
$|A| \cdot I = adj(A) \cdot A$
Taking determinant, we get
$|A|^n = |adj(A)| \cdot |A|$
$|adj(A)| = |A|^{n-1}$
So, option (a) is INcorrect.