Consider a 3×33 \times 33×3 orthogonal matrix QQQ (where QTQ=IQ^T Q = IQTQ=I). Which statement is FALSE?
det(Q)=±1\det(Q) = \pm 1det(Q)=±1
The columns of QQQ form an orthonormal basis of R3\mathbb{R}^3R3
QT=Q−1Q^T = Q^{-1}QT=Q−1
If QQQ is orthogonal, then all eigenvalues of QQQ are real numbers