Exercise 4.5.16

Determine whether $B$ is a right inverse, left inverse, both, or neither of $A$.

1. $$A=\left[\begin{array}{rrr}4&2&1\\ 2&1&1\\ \end{array}\right],\quad B=\left[\begin{array}{rrr}1&-1\\ -1&1\\ -1&2\\ \end{array}\right].$$
2. $$A=\left[\begin{array}{rrr}1&0\\ 0&1\\ 0&2\\ \end{array}\right],\quad B=\left[\begin{array}{rrr}1&2&-1\\ 0&1&0\\ \end{array}\right].$$
3. $$A=\left[\begin{array}{rrr}1&2\\ 3&7\\ \end{array}\right],\quad B=\left[\begin{array}{rrr}7&-2\\ -3&1\\ \end{array}\right].$$
4. $$A=\left[\begin{array}{rrr}1&2\\ 3&1\\ \end{array}\right],\quad B=\left[\begin{array}{rrr}-1&2\\ 1&-1\\ \end{array}\right].$$