Mathematics > algebra > Determinants

If $A$ is a $3\times3$ invertible matrix, show that for any scalar $k\ne0$, $(kA)^{-1}=\frac{1}{k}A^{-1}$. Hence calculate $(3A)^{-1}$, where $A=\begin{pmatrix}2&-1&1\\\\ -1&2&-1\\\\ 1&-1&2\end{pmatrix}$.