Determinant of an orthogonal matrix

If Q⊤Q=IQ^\top Q = I, what are the possible values of det⁡Q\det Q?

Show hints (2)+
  1. Take det⁡\det of both sides of Q⊤Q=IQ^\top Q = I.
  2. det⁡(Q⊤)=det⁡(Q)\det(Q^\top) = \det(Q).

Answer

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±1\pm 1

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