Determinant of a block anti-diagonal matrix Let $a = \begin{pmatrix}
O & \cdots & O & A \\
O &  \cdots& B & O\\
\vdots & \ddots & O & O\\
C & \dots &  O & O
\end{pmatrix}$,
where $A, B, C$ are $2n \times 2n $ matrices over ring of integers modulo $m$ that is, $\mathbb{Z}_m$. Is $det(a) = det(AB\dots C)?$

Think of rearranging the matrix, by swapping   columns, say, so that it becomes block diagonal. You will have to keep track of the signs.
