Part CCSIR NET December 2024over-the-reals-an-irreducible-quadratic-forces-even-degree

Over the reals an irreducible quadratic forces even degree

Which of the following statements are true?

A.There exists a 5 × 5 real matrix whose minimal polynomial is $(x^{2} + x + 1) x^{3}$ .✓
B.There exists a 5 × 5 real matrix whose minimal polynomial is $(x^{2} + x + 1)^{2}$ .
C.There exists a 5 × 5 complex matrix whose minimal polynomial is $(x^{2} + x + 1)^{2} x$ .✓
D.There exists a 5 × 5 complex matrix whose minimal polynomial is $(x^{2} + x + 1)^{2}$ .✓

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

50 are analysed free — try those first.

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