# Math Help - Angle of rotation and axis of rotation of a 3x3 matrix

1. ## Angle of rotation and axis of rotation of a 3x3 matrix

Hi,

I've been given a matrix X which is a 3x3 rotation matrix entries 2/3 -2/3 -1/3
1/3 2/3 -2/3
2/3 1/3 2/3
And I've found that $X^6=I$ Where I is the 3x3 identity matrix

I'm then asked to find the angle of rotation and axis of rotation, however i have no idea how to do this, and also I haven't been told what axis it's rotating about... :S.

Any help would be really appreciated thanks!.

2. ## Re: Angle of rotation and axis of rotation of a 3x3 matrix

the angle of rotation would be 2pi/6 = pi/3, because if 6 rotations are needed for a full rotation (no net effect = identity), then 6 times the angle of rotation = 2pi.
I'm not sure about the axis of rotation though.

EDIT: nvm I messed up. what I said is only true if X^6 = X, not X^6 = I, however, if X^6 = I, then X^7 = X, which means the angle of rotation is (2pi)/7 for similar reasons described above