Matrix and eigenvalue question

Question

If there are two square matrices, both the same size and they both have, say, eigenvalues of 1 and 2.
Matrix A has an eigenvalue of 1 with a multiplicity of 2 and an eigenvalue of 2 with a multiplicity of 1.
Matrix B has an eigenvalue of 1 with a multiplicity of 1 and an eigenvalue of 2 with a multiplicity of 2.

Would these two matrices be considered to have the same eigenvalues, or do the repeated values count?

Answer 1

This depends on the context in which you're interested in them having the same eigenvalues. As you've described quite well, the set of eigenvalues is the same, but the associated multiplicities are different.