If `a+b+c!=0` and `|(a, b, c),(b, c, a),(c,a,b)|=0` , then prove that `a=b=c`.

Explanation

To prove that if \( a + b + c \neq 0 \) and the determinant

\[
\begin{vmatrix}
a & b & c \\
b & c & a \\
c & a & b
\end{vmatrix} = 0
...