Linear Algebra - help with Eigenvalues!

[clouseu]

Hi! So I'm currently studying for my linear algebra final and I have encountered a question that has me stumped. Unfortunately I can't find anything online about to help me with it as well so here I am!
Now I was wondering first if someone could explain eigenvalues/eigenvectors to me just incase my understanding of them isn't right and if you could maybe help me with this question?

Question:
When E^2 = I (where I = nxn identity matrix and E denotes an nxn matrix) show that if λ is an eigenvalue of E then λ ϵ {±1}.

Any help at all would be appreciated! Many thanks in advance

 

[Deleted member 4993]

Hi! So I'm currently studying for my linear algebra final and I have encountered a question that has me stumped. Unfortunately I can't find anything online about to help me with it as well so here I am!
Now I was wondering first if someone could explain eigenvalues/eigenvectors to me just in case my understanding of them isn't right and if you could maybe help me with this question?

Question:
When E^2 = I (where I = nxn identity matrix and E denotes an nxn matrix) show that if λ is an eigenvalue of E then λ ϵ {±1}.

Any help at all would be appreciated! Many thanks in advance

Are you taking this class on-line?

What are your thoughts about the assigned problem? Please share your work - so that we know where to start.

 

[clouseu]

Are you taking this class on-line?

What are your thoughts about the assigned problem? Please share your work - so that we know where to start.

I'm studying the class in University, but the lecturer doesn't have any notes regarding the problem and is uncontactable at the moment.
I'm unsure about what the question is asking, I'm just generally not sure how to show that.

 

[Deleted member 4993]

I'm studying the class in University, but the lecturer doesn't have any notes regarding the problem and is uncontactable at the moment.
I'm unsure about what the question is asking, I'm just generally not sure how to show that.

What does your textbook say about eigenvalues and eigenfunctions?