Chapter 2.2, Problem 34E

One of the five given matrices represents an orthogonalprojection onto a line and another represents a reflection about a line. Identify both and briefly justify yourchoice.
$\begin{array}{l}A=\frac{1}{3}\left[\begin{array}{ccc}1& 2& 2\\ 2& 1& 2\\ 2& 2& 1\end{array}\right],B=\frac{1}{3}\left[\begin{array}{ccc}1& 1& 1\\ 1& 1& 1\\ 1& 1& 1\end{array}\right],\\ C=\frac{1}{3}\left[\begin{array}{ccc}2& 1& 1\\ 1& 2& 1\\ 1& 1& 2\end{array}\right],D=-\frac{1}{3}\left[\begin{array}{ccc}1& 2& 2\\ 2& 1& 2\\ 2& 2& 1\end{array}\right]\\ E=\frac{1}{3}\left[\begin{array}{ccc}-1& 2& 2\\ 2& -1& 2\\ 2& 2& -1\end{array}\right]\end{array}$