Here, $\mathbf{A} = \mathbf{A}$, $\mathbf{B} = \mathbf{B}$, and $\mathbf{C} = \mathbf{B}$. So, we have:
\[(\mathbf{A} \times \mathbf{B}) \times \mathbf{B} = (\mathbf{A} \cdot \mathbf{B})\mathbf{B} - (\mathbf{A} \times \mathbf{B})\mathbf{B}\]
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