I came across a vector term like
$$ \nabla \cdot (\nabla \times \mathbf{F}) = 0 $$
So I though to solve it like
\begin{align*}
M
&= \nabla \cdot (\nabla \times \mathbf{F}) \\
&= \mathbf{F} \cdot (\nabla \times \nabla) – \nabla \cdot (\nabla \times \mathbf{F}) \\
&= \mathbf{F} \cdot (\nabla \times \nabla) – M, \\
\vphantom{\Big(}
2M &= \mathbf{F} \cdot (\nabla \times \nabla) = 0.
\end{align*}
Here I suppose $\nabla \times \nabla$ must be zero. So
$$ \nabla \cdot (\nabla \times \mathbf{F}) = 0 $$
Is this is true that $\nabla \times \nabla$ (This is meaningless)?
Best Answer
From Wikipedia,