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Math Help - linear algebra inverses

  1. #1
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    linear algebra inverses

    Urgent help needed on the following question on matrices in linear algebra:

    Let A be an nxn square matrix such that A^2=0. Show that I+A is invertible and that (I+A)^-1=I-A.
    (Where I is the identity matrix).

    thanks
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  2. #2
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    Quote Originally Posted by smiler View Post
    Urgent help needed on the following question on matrices in linear algebra:

    Let A be an nxn square matrix such that A^2=0. Show that I+A is invertible and that (I+A)^-1=I-A.
    (Where I is the identity matrix).

    thanks
    To show that I+A is invertible you need to show that there is an inverse matrix. There is! The inverse matrix is I-A because (I+A)(I-A) = I^2 - A^2 = I^2 = I.
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