Term of rotation matrix entries equals 1 - proof concept?! I derived some stuff and it is happening that i come to the following expression:
$\frac{r_{13}^2 + r_{23}^2}{(r_{11}r_{23} - r_{13}r_{21})^2 + (r_{12}r_{23} - r_{13}r_{22})^2}$ 
that must equal 1 for all first two rows of a rotation matrix (orthogonal matrix).
$$  \begin{matrix}
    r_{11} & r_{12} & r_{13} & \\
    \end{matrix}   $$
$$  \begin{matrix}
 r_{21} & r_{22} & r_{23} & \\
    \end{matrix}   $$
I am confused how to proof this! I see a bit of a cross product in the denominator but can't identify the relation combined with the numerator.

The denominator shows the sum of squares of two components of a cross product, which are precisely the components of the vector at the denominator.
