Wedge Product of One-Form and Two-Form Reducing to Zero

Question

$w^{a}_{\;a} \wedge e^a = 0$

Where $w^{a}_{\;a}$ is a two-form, and $e^a$ is a one-form. Why does their wedge equal zero? Is it because $w^{a}_{\;a} = 0$ on its own?