Question

If any two adjacent rows or columns of a determinant are interchanged in position, the value of the determinant :

• A. Becomes zero
• B. Remains the same
• C. Changes its sign
• D. Is doubled

Answer 1

Answer: (C)

Changes its sign

If two rows or columns are interchanged

then the value of determinant changes its sign

$A=\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|$

Interchanging column

$B=\left|\begin{array}{cc}b& a\\ d& c\end{array}\right|A=-B$

Similarly, interchanging rows will give

$C=\left|\begin{array}{cc}c& d\\ a& b\end{array}\right|A=-C$

Hence, C is correct.