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Help understanding question

  1. Feb 26, 2004 #1
    What is the following question asking?


    Prove that the determinant of the product of two general 2x2 matrces is the product of their determinants.

    What I think is that I should come up with two 2x2 matrices.
    1 2 2 3 12 15
    3 4 and 5 6 multiply them together and get 26 33

    The determinant of the product matrix is six. The determinat of the first matrix is -2 and the second one is -3. Multiply -2 times -3 and that is 6. So I proved that the determinant of the product of the two matrices is the product of their determinants.

    Is this right?
  2. jcsd
  3. Feb 26, 2004 #2
    here are the matrices

    1 2 (1)
    3 4

    2 3
    5 6 (2)

    12 15
    26 33 (product matrix)
  4. Feb 26, 2004 #3


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    Homework Helper

    You should probably be more general (let the elements be letters instead of numbers, and then show it). It looks like you've got the right idea, though.
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