hi, this is my first time using this forum so if i have posted in the wrong place i do apologise!

I'm having trouble with a question on my matrices worksheet:

"Show directly from the definition of an eigenvalue that two similar matrices A and B have the same eigenvalues"

I've already done this by showing that they have the same characteristic polynomial but this is the second part of the question and you have to show it from the definition. I started by trying to show if Av=xv for an eigenvalue x and eigenvector v then P-1BPv=xv but I can't seem to get rid of the P next to the v!

someone suggested using basis(?) or something but we haven't learnt that yet so I'm not sure about that!

any help would be appreciated, thankyou.