Question:
Using properties of determinants prove that:
$\left|\begin{array}{ccc}3 x & -x+y & -x+z \\ x-y & 3 y & z-y \\ x-z & y-z & 3 z\end{array}\right|=3(x+y+z)(x y+y z+z x)$
Solution:
$=(x+y+z)(3 x y+3 y z+3 x z)$
$=3(x+y+z)(x y+y z+z x)$
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