Exercise 4.5.1

For each of the following pairs of matrices, determine whether $B$ is an inverse of $A$.

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