Find the matrices that reverse … and … and project: …M\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}y\\x\end{bmatrix}\quad\text{and}\quad P\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}x\\0\end{bmatrix}

Find the matrices that reverse $x$ and $y$ and project:
$$M\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}y\\ x\end{array}\right]\text{and}P\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}x\\ 0\end{array}\right].$$

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §11.4 Matrices and Linear Equations, #42