Determinant/Diagonal block matrix/No cross formula/Exercise

Let ${}M$ be a square matrix of the form

${}M={\begin{pmatrix}A&B\\C&D\end{pmatrix}}\,$

with square matrices ${}A,B,C$ and ${}D$. Show by an example that the equality

${}\det M=\det A\cdot \det D-\det B\cdot \det C\,$

does not hold in general.

Create a solution