Using properties of determinants, prove the following `|(3a,-a+b,-a+c),(a-b,3b,c-a),(a-c,b-c,3c)|=3(a+b+c)(ab+bc+ca)`

Explanation

To prove the determinant equation

\[
\left|
\begin{array}{ccc}
3a & -a + b & -a + c \\
a - b & 3b & c - a \\
a - c & b - c & 3c
...