Understanding Eigenvalues and Eigenvectors in Reflection Matrices

[Whiz]

Homework Statement

Let A be a matrix corresponding to reflection in 2 dimensions across the line generated by a vector v . Check all true statements:

A. lambda =1 is an eigenvalue for A
B. Any vector w perpendicular to v is an eigenvector for A corresponding to the eigenvalue lambda =1.
C. The vector v is an eigenvector for A corresponding to the eigenvalue lambda =1.
D. Any vector w perpendicular to v is an eigenvector for A corresponding to the eigenvalue lambda =−1.
E. lambda =−1 is an eigenvalue for A
F. None of the above

The Attempt at a Solution

I honestly have no clue how to do this question. Can somebody explain to me what the question is asking and how to solve it?

 

[Office_Shredder]

Do you know what the definition of an eigenvalue/eigenvector is? Think about the case where A just reflects over the x-axis first in R² in order to get a handle on what the question is asking