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 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?