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Let P be a non-singular matrix such that I + P + P 2 + … . . + P n = O (where O denotes the null matrix), then P - 1 is

Options

  1. AP n
  2. B- P n
  3. C- 1 + P + P 2 + … . + P n
  4. DNone of these

Correct answer

A. P n

Step-by-step solution

Given, I + P + P 2 + … … + P n = O P - 1 + P - 1 P + P - 1 P P + … … . + P - 1 P P n - 1 = O ⇒ P - 1 + I + I P + … … . . + I P n - 1 = O ⇒ P - 1 = P n

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