Let $M$ be a smooth manifold. Let $\mathcal \vartheta \in \mathfrak X^k (M)$ be a $k$-vector field and $\alpha \in \Omega^1 (M)$ be a $1$-form on $M.$ Then we define $i_{\alpha} \vartheta \in \mathfrak X^{k-1} (M)$ (the interior product of $\vartheta$ by $\alpha$) as follows $:$ $$i_{\alpha} \vartheta\ (\alpha_1, \cdots, \alpha_{k-1}) : = \vartheta\ (\alpha, \alpha_1, \cdots, \alpha_{k-1})$$ where $\alpha_1, \cdots, \alpha_{k - 1} \in \Omega^1 (M).$
With this definition in mind we have to show that given $\vartheta \in \mathfrak X^k (M)$ and $\zeta \in \mathfrak X^s (M)$ the following equality holds $:$ $$i_{\alpha} (\vartheta \wedge \zeta) = i_{\alpha} \vartheta \wedge \zeta + (-1)^k \vartheta \wedge i_{\alpha} \zeta.$$
Which I could not able to prove. Any help would be greatly appreciated.
Thanks for your time.