Einstein Summation Notation Interpretation A vector field is called irrotational if its curl is zero. A vector field is called solenoidal if its divergence is zero. If A and B are irrotational, prove that A $ \times $ B is solenoidal.
I'm having a hard time the proof equation that is required, and the steps that would go with it. I am defining V as a vector.
$ \nabla \times V = 0 $ = irrotational
$ \nabla \cdot V = 0 $ = solenoidal
$ \nabla \times A = 0 $
$ \nabla \times B = 0 $ 
so therefore, ($ \nabla \times A  $)+ ($ \nabla \times B) = \nabla \cdot (A \times B) $
would this be a correct setup? I'm having a hard time expanding this to E.S. form.

Note that your left side is a vector (which happens to be zero) and the right side is a scalar (which you are hoping to prove is zero) so they can't be equal .  The right side is $\varepsilon_{ijk}\frac d{dx_ i}A_jB_k$ while $\nabla \times A = 0$ is $\varepsilon_{ijk}\frac d{dx_i}A_j=0$ but those look a lot the same.  If you expand out the product you should be able to find a way to make use of the irrotational nature of $A$ and $B$.
