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Part CCSIR NET December 2023invertibility-from-matrix-identity

Invertibility from matrix identity

Let X, Y be two n × n real matrices such that XY . Which of the following statements are necessarily true?

  1. A.X is invertible.
  2. B.X + I is invertible.
  3. C.XY = YX.
  4. D.Y is invertible.

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The trap it tests

Execution slip

The idea was right. The computation was not.

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Related counterexample: Same characteristic polynomial ⇒ similar

More on this topic

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

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