Prove the identities:

a. \(abla \cdot(abla \times \mathbf{A})=0\).

b. \(abla \cdot(f abla g-g abla f)=f abla^{2} g-g abla^{2} f\).

c. \(abla r^{n}=n r^{n-2} \mathbf{r}, \quad n \geq 2\).