$(\mathbf{A} \times \mathbf{B})=\mathrm{AB} \sin \Theta$ û, where û is a unit vector perpendicular to both $A$ and $B$.

Now, $\mathbf{A} .(\mathbf{A} \times \mathbf{B})$ is basically a dot product between two vectors which are perpendicular to each other.

Then $\cos 90^{\circ}=0$, and thus

A. $(\mathbf{A} \times \mathbf{B})=0$