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Matrix inverse proof

  1. Sep 27, 2008 #1
    Show that A^-1 = -(1/3)((A^2) -2A -4I)

    In the question it gives you matrix A, so i presume the question just wants you to evaluate the right hand side.

    But can this be done with out just subbing in the matrix given?

    A = [1 0 1;2 3 4;-1 0 -2]
  2. jcsd
  3. Sep 27, 2008 #2


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    Staff Emeritus
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    What would evaluating the right side tell you? If the equation is correct, it should give you A-1. Have you already found that inverse? Simpler would be to evaluate the right side, then multiply that by A.

    But to answer your question, yes, that is exactly what "evaluate" means. If you were asked to evaluate the (numerical) polynomial -(1/3)(x2- 2x- 4) for x= 2, you would replace x by 2 and do the arithmetic. Same thing here.
    Last edited: Sep 27, 2008
  4. Sep 27, 2008 #3
    love you as always :)
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