Do eigenvalues remain the same after transforming a matrix to an upper diagonal one?

Question

If I transform a matrix to an upper diagonal one using elementary operations on rows, would the eigen values be the same between the transformed and the original matrix?

Answer 1

No, not in general.

For example, every invertible matrix (e.g. the diagonal matrix with entries 1 and 2) is row-equivalent to the identity, whose only eigenvalues are 1.