If QQQ is a 3×33 \times 33×3 orthogonal matrix (meaning QTQ=IQ^T Q = IQTQ=I), what are the possible values of det(Q)\det(Q)det(Q)?
Only 111
Only −1-1−1
Both 111 and −1-1−1
Any real number between −1-1−1 and 111