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Part BCSIR NET December 2024satisfying-a-polynomial-is-not-having-it-as-minimal

Satisfying a polynomial is not having it as minimal

Let A be a 3 × 3 complex matrix such that A3A^{3} is the identity matrix. Which of the following statements is true?

  1. A.A is diagonalizable.✓ Correct
  2. B.A has at least two distinct eigenvalues.
  3. C.The characteristic polynomial of A is x3−1x^{3} - 1.
  4. D.The minimal polynomial of A cannot have degree 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, and why this one tests invariants don't determine.

See pricing

50 are analysed free — try those first.

The trap it tests

Invariants don't determine

Two objects sharing an invariant were treated as the same object.

Drill statements like this

Related counterexample: Diagonalisable ⇒ invertible

More on this topic

The chapter behind this: Diagonalisability — the criteria card — free to read

From Eigenvalues and Canonical Forms › Diagonalisability criteria

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