# determinant of a rotation matrix

Posted by chaospixel
Announcements Last Post
SoC Curricula 09/30/2017 01:08PM
Demarcation or scoping of examinations and assessment 02/13/2017 07:59AM
School of Computing Short Learning Programmes 11/24/2014 08:37AM
Unisa contact information 07/28/2011 01:28PM
 determinant of a rotation matrix September 11, 2006 10:04PM IP/Host: 198.54.202.--- Registered: 14 years ago Posts: 78 Rating: 0
Why must the determinant of a rotation matrix be 1? I get that its inverse is its transpose and therefore it is orthonormal. but I don't get why that means its determinant is 1.
 Re: determinant of a rotation matrix September 11, 2006 11:15PM IP/Host: 198.54.202.--- Registered: 14 years ago Posts: 78 Rating: 0
The best I seem to be able to find online is that a rotation matrix is an orthogonal matrix with a determinant of 1. I also found out that any orthogonal matrix must have a determinant of either 1 or -1 because:

1 = det(I) = det(Q^T Q) = det(Q^T)det(Q) = (det(Q))^2 so det(Q) = +/-sqrt(1)

does anyone see _why_ an orthogonal matrix with a determinant of 1 _must_ rotate some things around some point by some angle?
Sorry, only registered users may post in this forum.