Why does det M = 1 mean rotation and det M = -1 mean reflection?

[neelakash]

We know that if M is an orthogonal matrix,then DetM=(+-)1
When Det M=1,thee transformation is a rotation.And for reflection about anyone o all three axes DetM=-1.
I did this..
But I did not know that information:When Det M=1,thee transformation is a rotation.And for reflection about anyone o all three axes DetM=-1.

Can anyone please justify this...
or give any link that can clarify the matter?

 

[mathwonk]

try dimwension three. and recall a cubic polynomila has a real root.