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Properties of Determinants : Orthogonal Matrix and Parallelepiped

If Q is an orthogonal matrix, so that QTQ = I, prove that det Q equals +1 or -1. What kind of parallelepiped is formed from the rows (or columns) of an orthogonal matrix Q?


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Determinants of an orthogonal matrix are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.