Proof of two similar matrices have same eigenvalue and a question

**Theorem:**

I've a question regarding the proof of a theorem.

There is a theorem in my linear algebra book that states:

"If and are similar x matrices, then they have the same eigenvalues."

**Proof of this theorem:**

Let and be similar matrices so there exist an invertible matrix such that

By the properties of determinant it follows that:

**My question:**

My question is: why is that

How do you proof that left hand side of this statement is equal to the right hand side?

What property of linear algebra makes this true? I can't figure out the answer for this problem. Is it possible help me finding the answer?

Re: Proof of two similar matrices have same eigenvalue and a question

What is ???

It is just I.

Re: Proof of two similar matrices have same eigenvalue and a question

Quote:

Originally Posted by

**dwsmith**

Thank you so much. I was thinking as a matrix(I don't know why I was thinking that). That was the error on my part. Sorry about that. Thanks for clarifying that using constant multiplication property of matrices.