The answer is below.
Work Step by Step
We know that the cross product of two vectors is a vector perpendicular to both. Thus, A cross B is perpendicular to A and B. Now, consider taking the dot product of A and A cross B. The dot product measures how parallel two vectors are. Since A cross B is perpendicular to A, this means that when we take the dot product of A and the result of the cross product, we will get 0.