Ononot — A matrix Q is orthogonal if Q^T Q = I. Taking determinants o

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Determinantshard

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A matrix $Q$ is orthogonal if $Q^T Q = I$ . Taking determinants of both sides: $\det(Q^T Q) = \det(I) = 1$ . Using $\det(Q^T) = \det(Q)$ , we get $[\det(Q)]^2 = 1$ . What are the possible values of $\det(Q)$ for any orthogonal matrix?