Chapter A.1, Problem 3P

Demonstrate that

$\text{A}=\left(\begin{array}{ccc}2& 2& 3\\ 1& 0& 1\\ 1& 1& 1\end{array}\right)$ and $\text{B}=\left(\begin{array}{ccc}-1& 1& 2\\ 0& -1& 1\\ 1& 0& -2\end{array}\right)$

are both nonsingular by showing that ${\text{AB=BA=I}}_{\text{3}}$