Thanks a lot, that's very useful!!
The problem I am trying to solve is listed below, it says "running", hopefully it works also with symbols
Where beta kappa sigma theta are all real numbers.
A11 = {{\[Beta] + \[Kappa]/\[Sigma], \[Kappa]}, {1/\[Sigma], 1}};
A21 = {{\[Theta]/(\[Sigma] . \[Sigma]) - \[Kappa]/\[Sigma] - \[Beta], \
\[Theta]/\[Sigma] - \[Kappa]}, {\[Beta] . \[Theta]/(\[Sigma] . \
\[Sigma]), \[Beta] . \[Theta]/\[Sigma]}};
A22 = {{1 + \[Kappa]/\[Sigma],
1}, {\[Beta] . \[Kappa]/\[Sigma], \[Beta]}};
Solve[A11 . c == c . A21 . c + c . A22 &&
Element[c, Matrices[{2, 2}]], c]