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Which are true?

  1. Mar 11, 2009 #1
    Which of these formulas hold for all invertible n x n matrices A and B:

    1) 8A is invertible
    2) A + B is invertible
    3) (A + B)^2 = A^2 + B^2 + 2AB
    4) (ABA^1)^7 = AB^7A^1
    5) (AB)^-1 = A^-1B^-1
    6) ABA^-1 = B

    Thanks
     
  2. jcsd
  3. Mar 11, 2009 #2
    For 1 and 2, why not see if you can find the inverse?

    For 3 multiply it out fist and tell me what you think

    For 4 multiply it out and it should be obvious.

    For 5 I'm sure you must have proved something for the left hand side. when you remove the brackets. How does it look like the right hand side?

    For 6 Right multiply by A. What did you learn about weather matrices commute?
     
  4. Mar 11, 2009 #3

    matt grime

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    This isn't a homework solution website. Please read the forum rules.
     
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