Question

If A = $\left|\begin{array}{ccc}ka& kb& kc\\ kd& ke& kf\\ kg& kh& ki\end{array}\right|$ and B = $\left|\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right|$ them A/B =

• A. 1
• B. k
• C. $k^3$
• D. $k^9$

Answer 1

The correct option is C $k^3$

t’s the property of the determinant that a scalar multiplied to a determinant will be same as the same scalar being multiplied to elements of one of the rows or columns of the same determinant. So if the scalar is multiplied to 3 rows or columns you can take out 3 times the scalar outside as below.

A = $\left|\begin{array}{ccc}ka& kb& kc\\ kd& ke& kf\\ kg& kh& ki\end{array}\right|$

= $k^3$$\left|\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right|$

Therefore, A/B = $k^3$