Let $X$ and $Y$ be vector fields, let $\omega$ be a $r$-form, and let $\eta$ be an $s$-form. Show that the following properties of the interior product are true:

(i) $i_{X} i_{Y} \omega=-i_{Y} i_{X} \omega$;

(ii) $i_{X}\left(\omega_{r} \wedge \eta_{s}\right)=\left(i_{X} \omega_{r}\right) \wedge \eta_{s}+(-1)^{r} \omega_{r} \wedge\left(i_{X} \eta_{s}\right)$.