Question
Prove that $\left[\begin{array}{lll}\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}} & \overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{c}} & \overrightarrow{\mathrm{c}}+\overrightarrow{\mathrm{a}}\end{array}\right]=2\left[\begin{array}{ll}\overrightarrow{\mathrm{a}} & \overrightarrow{\mathrm{b}} \overrightarrow{\mathrm{c}}\end{array}\right]$.