Which of the following statements is incorrect?

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

By the properties of determinants, Options (1), (2) and (3) are true: identical rows or columns give 0, a row of zeros gives 0, and \(|A^T| = |A|\).

Option (4) is false: interchanging two rows changes the sign of the determinant. For example:

    \( \displaystyle \begin{vmatrix} 1 & 2 \\ 3 & 4 \end{vmatrix} = 4 - 6 = -2 \)

    \( \displaystyle \begin{vmatrix} 3 & 4 \\ 1 & 2 \end{vmatrix} = 6 - 4 = 2 \)