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Shamsun posted an Question
September 01, 2020 • 07:39 am 30 points
  • IIT JAM
  • Mathematics (MA)

39 leta de an n x n matrix with real entries such that a? = a. if i denotes the n x n identity mati then show that rank(a - 1) = nullity (a). 39

39 LetA De an n x n matrix with real entries such that A? = A. If I denotes the n x n identity mati then show that rank(A - 1) = nullity (A). 39

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    Piyush pachauri

    Please let me know if any step is unclear. I have used some simple facts.

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    trace(A) =rank(A) ... how

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    Since diagonal elements are either 0 or 1 . Then trace implies no of non zero elements.

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    Hope you get it.

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