Question: Let A and B be n n matrices. Prove that the sum of all the eigenvalues of A + B is the sum of

Let A and B be n × n matrices. Prove that the sum of all the eigenvalues of A + B is the sum of all the eigenvalues of A and B individually. Prove that the product of all the eigenvalues of AB is the product of all the eigenvalues of A and B individually.

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