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Linear Algebra - Matrix Multiplication

  1. Feb 23, 2010 #1
    | 1 1 1 | = matrix A
    | 1 2 3 |
    | 1 4 5 |

    How do I find a 3x3 matrix B, excluding the identity or zero matrix, such that AB = BA?
  2. jcsd
  3. Feb 23, 2010 #2
    I think if you create and multiply by a diagonal matrix, it would work.
    I know for sure that if A and B are diagonal matrices, AB=BA
  4. Feb 23, 2010 #3
    You could make a matrix of entries a b c d e f g h i and let that be matrix B,and you can then multiply AB and BA, and equate each entry or make a system of equations out of it and find what value each letter has in terms of the other letters. There may be an easier way I'm tired.
  5. Feb 24, 2010 #4


    Staff: Mentor

    The inverse of A, A-1, is a matrix for which AA-1 = A-1A. Do you know how to find the inverse of a given matrix?
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