Reflect, Shear, Rotate

Three linear maps on $\mathbb{R}^2$:

$F = \begin{pmatrix}0 & 1\\ 1 & 0\end{pmatrix} \ \text{(reflection across } y = x)\qquad S = \begin{pmatrix}1 & 2\\ 0 & 1\end{pmatrix} \ \text{(horizontal shear)}\qquad R = \begin{pmatrix}0 & -1\\ 1 & 0\end{pmatrix} \ \text{(rotation } 90^\circ \text{ counter-clockwise)}$

A point $v$ is put through all three, in this order: first reflect with $F$, then shear with $S$, then rotate with $R$.

Find the single $2\times2$ matrix $M$ that performs the whole pipeline in one step, and the image of $v = \begin{pmatrix}3\\ 1\end{pmatrix}$ under it.