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

Question

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?

Answer 1

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

eg: take $R_{4}$ and do

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