Equivalent Definitions of Field Trace of Galois Extension

Question

When studying trace and norm of finite Galois extensions, I stumbled upon two (for Galois extensions) equivalent definitions.

1. $Tr_{L|K}(a) = tr(\phi_a)$ with $\phi_a: L \to L, x \mapsto ax$
2. $Tr_{L|K}(a) = \sum_{\sigma \in Gal(L|K)} \sigma(a)$

Could someone explain to me why those are equivalent? I'm having a hard time seeing the connection. Thank you a lot!!