If A and B are two non-singular matrices of order n, then which of the following statement/statements is/are not correct?

(A) AB is non-singular.
(B) AB is singular.
(C) $(AB)^{-1} = A^{-1} B^{-1}$
(D) $(AB)^{-1}$ does not exist.

Choose the correct answer from the options given below:

(B), (C) and (D) only

The correct answer is Option (4) → (B), (C) and (D) only

Given: A and B are non-singular (invertible) n×n matrices.

(A) AB is non-singular ✔ (product of invertible matrices is invertible)

(B) AB is singular ✖ (incorrect)

(C) $(AB)^{-1} = A^{-1}B^{-1}$ ✖ (incorrect; $(AB)^{-1} = B^{-1}A^{-1}$)

(D) $(AB)^{-1}$ does not exist ✖ (incorrect; it exists)