Chapter 2.2, Problem 33E

Use the algorithm from this section to find the inverses of

$\left[\begin{array}{ccc}1& 0& 0\\ 1& 1& 0\\ 1& 1& 1\end{array}\right]$ and $\left[\begin{array}{cccc}1& 0& 0& 0\\ 1& 1& 0& 0\\ 1& 1& 1& 0\\ 1& 1& 1& 1\end{array}\right]$.

Let A be the corresponding n × n matrix, and let B be its inverse. Guess the form of B, and then prove that AB = I and BA = I.