Exercise 2.1.17

$P=\left[\begin{array}{ccc}0\hfill & 1\hfill & 0\hfill \\ 0\hfill & 0\hfill & 1\hfill \\ 1\hfill & 0\hfill & 0\hfill \end{array}\right]$produces $\left[\begin{array}{c}y\hfill \\ z\hfill \\ x\hfill \end{array}\right]$and $Q=\left[\begin{array}{ccc}0\hfill & 0\hfill & 1\hfill \\ 1\hfill & 0\hfill & 0\hfill \\ 0\hfill & 1\hfill & 0\hfill \end{array}\right]$recovers $\left[\begin{array}{c}x\hfill \\ y\hfill \\ z\hfill \end{array}\right].Q$is the inverse of $P.$ Later we write $\mathit{QP}=I$ and $Q=P^{-1}$