Which of the following matrices is diagonalizable over R\mathbb{R}R?
C=(0−110)C = \begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}C=(01−10) (rotation matrix)
D=(1001)D = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}D=(1001) (identity matrix)
E=(2102)E = \begin{pmatrix} 2 & 1 \\ 0 & 2 \end{pmatrix}E=(2012) (Jordan block)
F=(010001000)F = \begin{pmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{pmatrix}F=000100010 (nilpotent)