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B Matrices concept confusion...

  1. Sep 29, 2016 #1
    In the photo that is a matrix B. B^3 + B = 2B^2 +2I from calculations. But why not B must be equal to 2I, the reason is as follow,
    B(B^2 + I ) = 2(B^2 +I)
    B(B^2 + I)(B^2 + I)^(-1) = 2I (B^2 + I)(B^2 + I)^(-1)
    so B = 2I why is my concept wrong? please explain to me.
     

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  2. jcsd
  3. Sep 29, 2016 #2

    phyzguy

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    Your concept assumes that the matrix (B^2 + I)^-1 exists. But there is also the possibility that the matrix (B^2 + I) is singular and has no inverse, which is the case for your matrix B.
     
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