Rotation and reflection matrices in $\mathbb{R}^2$

Consider the matrices \(A = { \left[ \begin{array} { l l } { \cos \phi } & { - \sin \phi } \\ { \sin \phi } & { \cos \phi } \end{array} \right] } , B = { \left[ \begin{array} { l l } { \cos \phi } & { \sin \phi } \\ { \sin \phi } & { - \cos \phi } \end{array} \right] }\)

1. Calculate \(A ^ { - 1 } , B ^ { - 1 }\)

2. Give a geometrical interpretation of the action of A and B on vectors in \(\mathbb { R } ^ { 2 }\)

3. What can one say about the eigenvectors of A and B?