Associator of Associative Algebra is Zero

Theorem
Let $\struct {A_R, \oplus}$ be an associative algebra.

Let $\sqbrk {a, b, c}$ denote the associator of $a, b, c \in A_R$.

Then:
 * $\forall a, b, c \in A_R: \sqbrk {a, b, c} = \mathbf 0_R$