# Matrix Determinant Calculation

I would like to solve the following question on matrix determinants. $$\begin{vmatrix} b+c&c+a&a+b\\b_1+c_1&c_1+a_1&a_1+b_1\\b_2+c_2&c_2+a_2&a_2+b_2\end{vmatrix} =X\begin{vmatrix} a&b&c\\a_1&b_1&c_1\\a_2&b_2&c_2\end{vmatrix} \;,\; X\in \mathbb{Z^+}$$ Determine the value of $X$.

Can someone please give an idea about the matrix manipulation required? Thanks!

$$\left( \begin{array}{ccc} a & b & c \\ a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ \end{array} \right) \left( \begin{array}{ccc} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{array} \right) = \; \; \; ????$$