# Reflection matrix

## 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

## 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

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tiny-tim
Homework Helper
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 does that mean it's a rotation and a reflection?
pi/3 will be the angle?

tiny-tim
Homework Helper
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

and if you combine them you get … ? 