Is it correct to write $\nabla\times(\nabla\times\textbf{E})$ as $\nabla\times(\nabla\times)\cdot\textbf{E}$?

Question

Is it correct to write $\nabla\times(\nabla\times\textbf{E})$ as $\nabla\times(\nabla\times)\cdot\textbf{E}$ ? I read this kind of expression on a book, but I wonder if it is correct to write it like this.

A

B