$\star$ is the Hodge star operator acting on differential $k$-forms on $\mathbb{R}^{n}$ as below:
$$\star:Λ^k(\mathbb{R}^{n}) \to Λ^{n-k}(\mathbb{R}^{n})$$ $$\alpha \wedge (\star \beta) = \langle \alpha,\beta \rangle \omega$$
where $ \langle , \rangle $ denotes the inner product on $(n-k)-$vectors and $\omega$ is the preferred unit $n-$vectors. Can somebody explain why we have
$$\star\star\omega=\left(-1\right)^{k\left(n-k\right)}\omega.$$