For a square matrix $A_{n \times n}$

(A) $|adj A|=|A|^{n-1}$
(B) $|A|=|adj A|^{n-1}$
(C) $A(adj A)=|A|$
(D) $\left|A^{-1}\right|=\frac{1}{|A|}$

Choose the correct answer from the options given below:

(A) and (D) only

The correct answer is Option (2) → (A) and (D) only

(B) is wrong

as $|adj\,A|=|A|^{n-1}$

(C) is wrong

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

(A), (D) already correct