Suppose $T$ is the linear transformation which rotates by $30°$ counterclockwise about the origin.

1. Write the matrix associated with $T$.

   Hint (a):

   Review your work from problem 12-39.

   Step (a):

   $\left[ \begin{array} { c c } { \operatorname { cos } 30 ^ { \circ } } & { \operatorname { sin } 30 ^ { \circ } } \\ { - \operatorname { sin } 30 ^ { \circ } } & { \operatorname { cos } 30 ^ { \circ } } \end{array} \right]$

2. Find $T ^{−1}$.

   Step (b):

   $\left[ \begin{array} { c c } { \operatorname { cos } 30 ^ { \circ } } & { \operatorname { sin } 30 ^ { \circ } } \\ { - \operatorname { sin } 30 ^ { \circ } } & { \operatorname { cos } 30 ^ { \circ } } \end{array} \right] \left[ \begin{array} { l l } { a } & { b } \\ { c } & { d } \end{array} \right] = \left[ \begin{array} { l l } { 1 } & { 0 } \\ { 0 } & { 1 } \end{array} \right]$