Let $M$ a manifold of class $C^{\infty}$. Show that $M$ is orientable if and only if $M \setminus \{p\}$ is orientable.
Comments:
($\Rightarrow$) Let $\omega: M \longrightarrow \Lambda^n(M)$ a orientation form of M then $\omega: M\setminus\{p\} \longrightarrow \Lambda^n(M\setminus\{p\})$ is a form which is never null then defines a orientation in $M\setminus\{p\}$.
I am having difficulty justifying the ($\Leftarrow$).