Prove, using the properties of determinants $\begin{bmatrix} a+b & b+c & c+a \\ b+c & c+a & a+b \\ c+a & a+b & b+c \end{bmatrix} = 2 \begin{bmatrix} a & b & c \\ b & c & a \\ c & a & b \end{bmatrix}$

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