Kunze Linear Algebra · Problem 5.4.4

Determinants

Mathematics — Methods · orthogonal-matrices-determinant

Problem

An n×nn \times n matrix AA over a field FF is called orthogonal if AAt=IAA^t = I. If AA is orthogonal, show that det⁡A=±1\det A = \pm 1. Give an example of an orthogonal matrix for which det⁡A=−1\det A = -1.

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