For n > 1, the maximum multiplicity of any eigenvalue of an n × n matrix with elements from R is

GATE CSE 2026 Session 1 Q13: Maximum multiplicity of an eigenvalue of an n×n real matrix

For $n > 1$ , the maximum multiplicity of any eigenvalue of an $n \times n$ matrix with elements from $\mathbb{R}$ is

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Answer: A (official GATE 2026 final answer key)

Concept used: The characteristic polynomial has degree $n$ , so an eigenvalue can repeat at most $n$ times.

First step: Think of the identity matrix: its eigenvalue 1 has multiplicity $n$ .

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Source: official GATE 2026 Session 1 CS question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key