solenoidal vector field times -1

Question

Given a solenoidal vector field $A$, is $A*(-1)$ also solenoidal?

In other words if $\nabla \cdot A = 0$.

Does $\nabla \cdot (-A) = 0 $ also?

Answer 1

Yes, $\nabla \cdot (c \mathbf{F}) = c (\nabla \cdot \mathbf{F})$ because $\nabla$ is a linear operator.