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Math Help - Identity Matrices

  1. #1
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    Identity Matrices

    i have this question and im havint trouble solving it, anyone have any idea?

    A matrix A obeys the matrix equation A3=2A + I where I is the identity matrix of appropriate order. The inverse A1 Is given by :

    any help would be much appreciated!
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  2. #2
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    Quote Originally Posted by sebko View Post
    i have this question and im havint trouble solving it, anyone have any idea?

    A matrix A obeys the matrix equation A3=2A + I where I is the identity matrix of appropriate order. The inverse A1 Is given by :

    any help would be much appreciated!
    Left multiply both sides of the expression by the inverse matrix:

    A^3 = 2A + I \Rightarrow A^2 = 2I + A^{-1}.
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