Solving Reflection Matrix Homework: Angle & Rotation About Origin

[Lchan1]

Homework Statement

Given the matrix A=
-1/2 root(3)/2
root(3)/2 1/2

determine if the matrix is a rotation about the origin or a reflection about the positive x axis
and find the angle between the that the line makes with the x-axis

Homework Equations

The Attempt at a Solution

I found the det(A)=-1 can I concluded that the matrix reflects vectors?
and also how do you find the angle?
I tried doing projection onto the axis. but didnt get me anywhere
please help..

 

[tiny-tim]

Hi Lchan1!

(have a square-root: √ )

I found the det(A)=-1 can I concluded that the matrix reflects vectors?

Yup!

and also how do you find the angle?

learn this:

rotation through angle θ is

cosθ sinθ
-sinθ cosθ

 

[Lchan1]

does that mean it's a rotation and a reflection?
pi/3 will be the angle?

 

[tiny-tim]

does that mean it's a rotation and a reflection?
pi/3 will be the angle?

sorry, I was a bit too cryptic last time

a combination of a rotation and a reflection is a reflection …

it would have been better if I'd said

rotation through angle θ is

cosθ sinθ
-sinθ cosθ

reflection about y-axis is

-1 0
0 1

and if you combine them you get … ?