Which of the following statements are correct ?

(A) If elements of a row (or column ) of a determinant are multiplied with cofactors of any other row( or column), then their sum is zero.

(B) The value of determinant is equal to the sum of the product of elements of any row (or column) with their corresponding cofactors.

(C) If any two rows (or columns) of a determinant are interchanged, their sign of determinant does not change.

(D) The value of determinant remains unchanged if its rows and columns are interchanged.

(E) A square matrix A has inverse if and only if A is singular.

Choose the correct answer from the options given below :

(A), (B), (D) Only

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

For (C) → If two rows/columns are changed then sign of determinant must change. 

For (E) → $A^{-1}$ exists iff A is NOT singular.