Question

The inverse of $\left[\begin{array}{ccc}1& 2& 2\\ 0& 1& 2\\ 0& 0& 1\end{array}\right]$ is

Answer 1

Given $A=\left[\begin{array}{ccc}1& 2& 2\\ 0& 1& 2\\ 0& 0& 1\end{array}\right]$
$|A|=\left|\begin{array}{ccc}1& 2& 2\\ 0& 1& 2\\ 0& 0& 1\end{array}\right|=1$
$AdjA=\left[\begin{array}{ccc}1& -2& 2\\ 0& 1& -2\\ 0& 0& 1\end{array}\right]$
$\therefore A^{-1}=\left[\begin{array}{ccc}1& -2& 2\\ 0& 1& -2\\ 0& 0& 1\end{array}\right]$