16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 6.5.4

Elementary Canonical Forms

Mathematics — Linear Algebra · determinant-block-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).

Browse the problem library