If A and B are square matrices of the same order, then which of the following statements are correct?

(A) $|A^{-1}|=|A|^{-1}$
(B) $\text{adj (A)} = |A|A^{-1}$
(C) $(A+B)^{-1}= B^{-1} + A^{-1}$
(D) $(AB)^{-1}= B^{-1}A^{-1}$

Choose the correct answer from the options given below:

(A), (B) and (D) only

The correct answer is Option (1) → (A), (B) and (D) only

Given A and B are square matrices of same order.

(A)$|A⁻¹| = 1 / |A| $✔ (Correct)

(B) $adj(A) = |A| A⁻¹ ✔ (Correct, since A⁻¹ = adj(A)/|A| → adj(A) = |A| A⁻¹)$

(C) $(A + B)⁻¹ = A⁻¹ + B⁻¹ $❌ (Incorrect in general)

(D) $(AB)⁻¹ = B⁻¹ A⁻¹ $✔ (Correct)