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How many 2x2 matricies equal I?

  1. Nov 18, 2009 #1
    Assuming A is a 2x2 matrix how many different matricies exist such that A^2=I ?
    I am 99% sure the answer is 4 but after putting that down as an answer with supporting evidence I was marked wrong (or atleast not fully correct) so I am stumped as to where to jump and whether or not the grader may ahve just messed up.
     
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  3. Nov 18, 2009 #2

    Hurkyl

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    Well, what was your attempt at proof?
     
  4. Nov 18, 2009 #3

    D H

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    The grader gave you partial credit because you got the wrong answer but showed the supporting evidence that led you down the wrong path. Consider this matrix:

    [tex]A = \bmatrix 0.6 & \phantom{-}1.6 \\ 0.4 & -0.6\endbmatrix[/tex]


    There are many, many more of such. Show your logic so we can help show where you went wrong.
     
  5. Nov 18, 2009 #4
    I got 4 equations,

    x^2 +yz=1
    xy+yw=0
    zx+wz=0
    zy+w^2=1.

    How do I solve this now?
     
  6. Nov 18, 2009 #5

    D H

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    Both of the middle equations (the ones equal to zero) have a common term. For example, xy+yw=0 is the same as (x+w)*y = 0. This means that at least one of x+w or y must be equal to zero. I suspect your four solutions result from setting y and z to zero. What if x+w=0?
     
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