Using the property of determinants and without expanding, prove that:`|[a-b,b-c,c-a],[ b-c,c-a ,a-b ],[c-a ,a-b,b-c]|=0`

Explanation

To prove that the determinant

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