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Homework Help: Finding 2 2x2 matrices resulting in -1

  1. Feb 2, 2009 #1
    1. The problem statement, all variables and given/known data
    Find two different 2×2 matrices (other than ±I) such that A.AT = I.

    Definition: I is referring to i^2=-1 axion
    AT=Transpose of A

    2. Relevant equations

    3. The attempt at a solution
    Trying to make matrices on paper so that A times the transpose of A gives me -1 in all rows and columns.
  2. jcsd
  3. Feb 2, 2009 #2
    Have you tried just writing out a matrix A with enries a,b,c,d, what would A^T look like then? Then multiply it out and set equal to I?

    I'm not sure what you mean by "I is refering to i^2 = -1". I thought by "I" you meant the identity matrix?
  4. Feb 2, 2009 #3
    No, there's an axion in mathematics apparently where the variable "i squared" (i^2) equals -1. The reason I wrote a Capital I is because I'm working with a program called Maple. It's the same thing, but in the two matrices that I have to find, I can't use the -1 axion.

    Sorry for the confusion.
  5. Feb 2, 2009 #4
    Yes but i^2 = -1 is an imaginary/complex number. You are working with matrices where I refers to the identity matrix.
  6. Feb 2, 2009 #5
    ......well I feel stupid as all...

    lol thx for clearing that up. ^^;
  7. Feb 2, 2009 #6


    Staff: Mentor

    No, i^2 is not imaginary. i is, though:biggrin:
  8. Feb 2, 2009 #7
    Haha, yes.
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