Discussion
For \(n \gt 1\), the maximum multiplicity of any eigenvalue of an n × n matrix with elements from \(\mathbb{R}\) is
Answer: A
The maximum multiplicity is n.
The characteristic polynomial of an n × n matrix has degree n, so no eigenvalue can be a root more than n times, which rules out n + 1.
The bound n is reached: the identity matrix, or any \(cI\), has the single eigenvalue c with multiplicity n. So the maximum is n, not n - 1 or 1.
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