I am trying to build two non-zero square matrices $A$ and $B$ whose product will be zero and who will have any fixed determinant value (e.g. det$(A) = 5$).
I can easily think of two non-zero square matrices that satisfy $AB = 0$, but to get them to have a specific determinant is tripping me up.
Would anyone know of a first step? I imagine it would be easy to start with two triangular matrices.