If AAA is an orthogonal matrix, which of the following must be true?
det(A)=±1\det(A) = \pm 1det(A)=±1
∣∣Ax∣∣=∣∣x∣∣||Ax|| = ||x||∣∣Ax∣∣=∣∣x∣∣
AT=A−1A^T = A^{-1}AT=A−1
All eigenvalues λ\lambdaλ satisfy ∣λ∣=1|\lambda| = 1∣λ∣=1