Question on indefinite special orthogonal group I'm stuck on this question:
Construct an element $x \in SO(1,2)$ which is not diagonalizable.
Any help would be appreciated

The group $SO(1,2)$ is isomorphic to $SL_2(\mathbb{R})$, which is perhaps more convenient to describe elements which are not diagonalisable over $\mathbb{R}$, such as parabolic or elliptic conjugacy classes, see here. For example, take
$$
g=\begin{pmatrix} 1 & 1 \cr 0 & 1 \end{pmatrix}.
$$
