# Matrix with given condition $a+b+c+d=0$ [closed]

Show that if $$a+b+c+d=0$$ then $$\begin{vmatrix} a &b &c &d \\ b & c & d & a\\ c& d& a& b\\ d& a& b& c \end{vmatrix}=0$$.

How can I do this?

## 1 Answer

Hint: Take any single row and add up all other rows onto it.

eg: take $$R_{4}$$ and do

$$R_{4} \to R_{4} + R_{3} + R_{2} + R_{1}$$

• comment: works for column as well Oct 1, 2020 at 11:55