Let A and B be two matrices different from I such that AB = BA and A n – B n is…

Mathematics · JEE Advanced · NTA ExamsMatrices and Determinants

Let A and B be two matrices different from I such that AB = BA and An – Bn is invertible for some positive integer n. If An – Bn = An + 1 – Bn + 1 = An + 2 – Bn + 2, then
  1. I – A is singular
  2. I – B is singular
  3. A = B
  4. (I – A) (I – B) is non-singular

Answer

(A) I – A is singular, (B) I – B is singular

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