Which of the following transformations are linear? Select all of the linear transformations. There may be more than one correct answer. Be sure you can justify your answers.

A. $T(A)=ASA^{-1}$ from ${\mathbb R}^{2 \times 2}$ to ${\mathbb R}^{2 \times 2}$, where $S=\left[\begin{array}{cc} -1 &9\cr 2 &-6 \end{array}\right]$

B. $T(A)=A \left[\begin{array}{cc} -9 &5\cr 1 &3 \end{array}\right]$ from ${\mathbb R}$ to ${\mathbb R}^{2 \times 2}$

C. $T(A)=A^{5}$ from ${\mathbb R}^{5 \times 5}$ to ${\mathbb R}^{5 \times 5}$

D. $T(A)= \mathrm{trace}(A)$ from ${\mathbb R}^{4 \times 4}$ to ${\mathbb R}$

E. $T(A)=A \left[\begin{array}{cc} 4 &-2\cr 6 &1 \end{array}\right] - \left[\begin{array}{cc} 4 &2\cr 6 &8 \end{array}\right] A$ from ${\mathbb R}^{2 \times 2}$ to ${\mathbb R}^{2 \times 2}$

F. $T(A)=\left[\begin{array}{cc} 1 &7\cr -4 &6 \end{array}\right] A$ from ${\mathbb R}^{2 \times 3}$ to ${\mathbb R}^{2 \times 3}$