We have,
\(\begin{vmatrix}
a & b & c \\[0.3em]
b & c & a \\[0.3em]
c & a & b
\end{vmatrix}=0\)
Applying C1 \(\longrightarrow\)C1+ C2 +C3,we get
Taking (a + b + c) common from C1, we get
Applying R2 \(\longrightarrow\) R2 - R1 and R3 \(\longrightarrow\) R3 - R1, we get
Expanding along C1, we get