Counterexample

Is this true?

Diagonalisable ⇒ invertible

No — it is false.

The counterexample

The object that kills this claim comes with Trap Analysis.

86 counterexamples are free — including most of the ones Part C leans on hardest.

Keep practicing

Invariants don't determine

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

See real exam options built on this mistake Drill statements like this

Go deeper· Explained in full in Diagonalisability — the criteria card· Asked in CSIR NET December 2025· From Eigenvalues and Canonical Forms › Diagonalisability criteria

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