Show that the $\mathcal{F}^4(f)=f$ for all $f\in \mathscr{S}(\mathbb{R})$

Question

I have some troubles with the following problem:

Consider the Schwartz space $\mathscr{S}(\mathbb{R})$, and view the Fourier transform as a linear map $\mathcal{F}:\mathscr{S}(\mathbb{R})\to \mathscr{S}(\mathbb{R})$.

Show that the $\mathcal{F}^4(f)=f$ for all $f\in \mathscr{S}(\mathbb{R})$

I have computed $\mathcal{F}^2(f)(x)=\int_\mathbb{R} f(x)e^{ix\xi} dm(x)=F^{*}(f)(\xi)$ which is the inverse Fourier transform. Now I am thinking I need to compute $F^{2}(F^{2}(f))$ but I don't know how to compute this so I get $f$.