Please, how can I find the determinant of the following matrix?
$$P=\left( \begin{array} {c,c} A \quad B \\ C \quad 0 \end{array} \right)$$
where $A$ is a 2x2 block matrix, $B$ is a 2x1 matrix, $C$ is a 1x2 matrix and $0$ is a 1x1 zero matrix.
Such that $$A=\left( \begin{array} {c,c,c} A_{11} \quad A_{12}\quad B_{11} \\ A_{21} \quad A_{22} \quad B_{21}\\ C_{11} \quad \, C_{12} \quad \, 0 \end{array} \right)$$
I know that for $$P=\left( \begin{array} {c,c} A \quad B \\ C \quad 0 \end{array} \right)$$ where $A$, $B$ and $C$ are $n\times n$ matrices, and $0$ is the $n\times n$ zero matrix $$\det(P)=\det(-C)\det(B)$$ What will $\det P$ be for unequal dimension block matrices?