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Math Help - Help on a matter involving matrices and determinants

  1. #1
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    Help on a matter involving matrices and determinants

    I have tried many ways to solve an issue, but I have not had a good success. The question is one that follows:

    A is a matrix of order 3x3. B is a matrix of order 2X3


    A=B^T*B (A is equal B transpose multiplied by B)

    Calculate the determinant of A^2 for any matrix A of order 3X3
    .

    I tried to be as direct as possible. I thank you for your help!
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  2. #2
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    "Caculate the determinant of A^2 for any matrix A of order 3X3" does not seem to have anything to do with "A= B^T*B".

    Did you mean "Calculate the determinant of A^2 for any matrix A, of the form A= B^T*B for some matrix B, of order 3X3"?

    It will help to know that det(AB)=det(A)det(B), so that det(A^2)= (det(A))^2 and perhaps that det(B^T)= det(B).
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  3. #3
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    I agree, to calculate the determinant of A^2 for any matrix of order 3X3. However, A must be A=B^T*B e B is a matrix of order 2X3.
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