Using properties of determinants. Prove that`|[3a,-a+b,-a+c],[-b+a,3b,-b+c],[-c+a,-c+b,3c]|=3(a+b+c)(a b+b c+c a)`

Explanation

To prove that

\[
| \begin{bmatrix}
3a & -a + b & -a + c \\
-b + a & 3b & -b + c \\
-c + a & -c + b & 3c
\end{bmatrix} | = 3(a + b + c)(ab + bc + ca),
...