If we have a matrix like:
$A_{12\times 12}=\left[ \begin{matrix} {{\Gamma }_{1}} & \mathbf{0_{5\times 6}} \\ {{\Gamma }_{2}} & {{\mathbf{G}}_{2}} \\ \mathbf{0_{5\times6}} & {{\mathbf{G}}_{1}} \\ \end{matrix} \right]$
where the matrices dimensions are as follows:
$\Gamma_1: 5\times 6$
$\Gamma_2: 2\times6$
$\mathbf{G}_2: 2\times6$
$\mathbf{G}_1: 5\times6$
is it possible to write $det(A)$ in terms of $\Gamma_1, \Gamma_2$ and $\mathbf{G}_1$, $\mathbf{G}_2$?
