Chapter 7, Problem 122RE

To determine

Whether the provided identity $\left|\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\\ a_{31}+c_1& a_{32}+c_2& a_{33}+c_3\end{array}\right|=\left|\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\\ a_{31}& a_{32}& a_{33}\end{array}\right|+\left|\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\\ c_1& c_2& c_3\end{array}\right|$ holds true or not. Describe with justification.