Select all of the linear transformations from ${\mathbb R}^3$ to ${\mathbb R}^3$ that are invertible. There may be more than one correct answer.

A. Trivial transformation (i.e. $T(\vec{v})=\vec{0}$ for all $\vec{v}$)
B. Identity transformation (i.e. $T(\vec{v})=\vec{v}$ for all $\vec{v}$)
C. Reflection in the $z$-axis
D. Rotation about the $y$-axis
E. Projection onto the $x$-axis
F. Dilation by a factor of $3$