Kunze Linear Algebra · Problem 6.5.4

Elementary Canonical Forms

Mathematics — Methods · determinant-block-matrix-commuting

Problem

Let AA, BB, CC, and DD be n×nn \times n complex matrices which commute. Let EE be the 2n×2n2n \times 2n matrix E=[ABCD].E = \begin{bmatrix} A & B \\ C & D \end{bmatrix}. Prove that det⁡E=det⁡(AD−BC)\det E = \det(AD - BC).

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