Which of the following statements is incorrect?

If any two rows of a determinant are interchanged, then the sign of the determinant remains unchanged.

The correct answer is Option (4) → If any two rows of a determinant are interchanged, then the sign of the determinant remains unchanged.

(A) If two rows or two columns of a determinant are identical, then the value of the determinant is zero.

This is a standard property of determinants.

Correct

(B) If all the elements in any one row of the determinant are zero, then the determinant value is zero.

This is also a standard property.

Correct

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

The value of the determinant is equal to the determinant of its transpose, hence this is correct.

Correct

(D) If any two rows of a determinant are interchanged, then the sign of the determinant remains unchanged.

Interchanging any two rows changes the sign of the determinant.

This statement is false.

The incorrect statement is (D).