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If AB=I, then A is invertible. False

  1. Apr 30, 2010 #1
    If AB=I, then A is invertible.

    False, but not sure how to show it.
     
  2. jcsd
  3. Apr 30, 2010 #2

    Mark44

    Staff: Mentor

    There's no requirement that A and B have to be square matrices. I came up with a 2x3 matrix and a 3x2 matrix whose product is I, a 2x2 matrix, yet neither of the matrices in the product is invertible.
     
  4. Apr 30, 2010 #3
    Thanks, I figured out a matrix that works.
     
  5. Nov 13, 2011 #4
    If A(n*n) and B (n*n).
    and If AB=I.
    is A invertible?
    is B inverse of A?
     
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