True or False? If A is an n × n matrix, P is an n × n invertible matrix, and B = P −1AP, then
a11 + a22 + . . . + ann = b11 + b22 + . . . + bn
Diagnolization, similar matrixes
The Attempt at a Solution
the question is asking if the summation of the main diagnols of A and B are the same. B is known to be similar to A since B = P^-1 AP. I can't find a counterexample, so I am assuming the summation of the diagnols of both are in fact equal, but this is hardly a proof. I know A and B share the same determinant, rank, and eigenvalues and rank, but I'm not sure how these relate to the main diagnol of the matrices.