Exercise 7.5.1

Let

An operation is done to get from $A$ to a matrix $B$. In each case, identify which operation was done and explain how it will affect the value of the determinant.

1. $$B=\left[\begin{array}{cc}a&c\\ b&d\\ \end{array}\right]$$
2. $$B=\left[\begin{array}{cc}c&d\\ a&b\\ \end{array}\right]$$
3. $$B=\left[\begin{array}{cc}a&b\\ a+c&b+d\\ \end{array}\right]$$
4. $$B=\left[\begin{array}{cc}a&b\\ 2c&2d\\ \end{array}\right]$$
5. $$B=\left[\begin{array}{cc}b&a\\ d&c\\ \end{array}\right]$$