Question

If value of $\left|\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right|$ is A then value of $\left|\begin{array}{ccc}d& e& f\\ a& b& c\\ g& h& i\end{array}\right|$ is equal to

• A. A
• B. -A
• C. 0.0
• D. 2A

Answer 1

The correct option is B -A

This is based on the property of determinants that if you interchange a pair of rows or columns in a matrix the determinant of the resulting matrix will be the negetive of the determinant of the original matrix. Here you can see that the second determinant is arrived by interchanging first and second rows. Hence the resulting second determinant is the negetive of the determinant of the first matrix.
Thus, $\left|\begin{array}{ccc}d& e& f\\ a& b& c\\ g& h& i\end{array}\right|=-A$