Exercise 4.3.18

For the first case, let $A$ be a matrix of type 2 meaning multiplying the $i$-th row by a scalar $c$. We have $\det <!--\; FUNCTION\; APPLICATION\; -->(A)=c$ by Exercise 4.2.28. And since determinant is linear function of the $i$-th row when other rows are held fixed, we have

For the second case, let $A$ be a matrix of type 3 meaning adding $c$ times the $i$-row to the $j$-th row. We have $\det <!--\; FUNCTION\; APPLICATION\; -->(A)=1$ by Exercise 4.2.28. And since determinant will not change when we adding some times the $i$-row to the $j$-th row, we have