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Part BCSIR NET December 2024abc-equals-one-makes-the-cycle-close

Abc equals one makes the cycle close

Let A = [[0, a, 0], [0, 0, b], [c, 0, 0]], where a, b, c are real numbers with abc = 1. If B=A+A2+A3B = A + A^{2} + A^{3}, then which of the following statements is true?

  1. A.det B = 1
  2. B.det A = 0
  3. C.rank(B) = 2
  4. D.rank(B2)=1rank(B^{2}) = 1✓ Correct

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 execution slip.

See pricing

50 are analysed free — try those first.

The trap it tests

Execution slip

The idea was right. The computation was not.

Drill statements like this

Related counterexample: Same characteristic polynomial ⇒ similar

More on this topic

The chapter behind this: Characteristic vs minimal polynomial — what each tells you — free to read

From Eigenvalues and Canonical Forms › Eigenvalues, characteristic & minimal polynomials, Cayley–Hamilton

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