Chapter 4.2, Problem 9E

Find out which of the transformations in Exercises 1 through 50 are linear. For those that are linear, determine whether they are isomorphisms.

9. $T\left(M\right)=S^{-1}MS$ , where $S=\left[\begin{array}{cc}3& 4\\ 5& 6\end{array}\right]$ from ${ℝ}^{2\times 2}$ to ${ℝ}^{2\times 2}$