If A is a $3 \times 3$ invertible matrix, show that for any scalar $k \neq 0$, $(kA)^{-1} = \frac{1}{k} A^{-1}$. Hence calculate $(3A)^{-1}$, where $A = \begin{bmatrix} 2 & -1 & 1 \\ -1 & 2 & -1 \\ 1 & -1 & 2 \end{bmatrix}$.