Chapter 3.2, Problem 43E

Proof Prove the property.

$\left|\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\\ a_{31}& a_{32}& a_{33}\end{array}\right|+\left|\begin{array}{ccc}{b}_{11}& a_{12}& a_{13}\\ b_{21}& a_{22}& a_{23}\\ b_{31}& a_{32}& a_{33}\end{array}\right|=\left|\begin{array}{ccc}\left(a_{11}+b_{11}\right)& a_{12}& a_{13}\\ \left(a_{21}+b_{21}\right)& a_{22}& a_{23}\\ \left(a_{31}+b_{31}\right)& a_{32}& a_{33}\end{array}\right|$