Find a matrix with determinant equals to $\det{(A)}\det{(D)}-\det{(B)}\det{(C)}$

Note: This answer is wrong, as indicated by the comments below.

Let $M \oplus N$ denote the block-diagonal matrix $$ M \oplus N = \pmatrix{M&0\\0&N} $$ Then one solution with $m = 4n$ is $$ E = \pmatrix{A \oplus I & I \oplus B\\I \oplus C & D \oplus I} $$ where $I$ denotes the $n \times n$ identity matrix.

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Linear Algebra

Matrices

Determinant

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