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Math Help - matrix inversion proof

  1. #1
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    matrix inversion proof

    Let A be an n \times n matrix such that A^k = 0_{n,n} (the n \times n zero matrix)
    for some natural integer k. Show that I _{n} + A is invertible.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    (I_n+A)(I_n-A+A^2-\ldots+(-1)^{k-1}A^{k-1})=\ldots=I_n .

    P.S. There is another way of proving it using theory of eigenvalues.
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