Chapter 3.CR, Problem 46CR

To determine

To prove:

The given property $\left|\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\\ a_{31}+c_{31}& a_{32}+c_{32}& a_{33}+c_{33}\end{array}\right|=\left|\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\\ a_{31}& a_{32}& a_{33}\end{array}\right|+\left|\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\\ c_{31}& c_{32}& c_{33}\end{array}\right|$ for the given condition $A=\left|\begin{array}{ccc}1& 0& 2\\ 1& -1& 2\\ 2& 1& -1\end{array}\right|$, $c_{31}=3,c_{32}=0,c_{33}=1$.