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Math Help - Help with a Linear Algebra - Matrices assignment..

  1. #1
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    Help with a Linear Algebra - Matrices assignment..

    Hi There,

    I've just been handed an assignment that I have no clue how to do..

    I will show you some of the questions below but I am not looking for straight answers. I would like some pointers on how to go about solving these where to get help.

    Introduction
    Show if the folowing statements are true or false for 2 x 2 matrices.

    1)
    det(AB) = det(A)det(B)
    2)
    det(A^-1)= 1(over)det(A)
    3)
    det(A^T)=det(A)

    Any advice would be greatly appreciated as this is due in one week and I have no clue how to go about this?

    Thanks..
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  2. #2
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    Quote Originally Posted by atwarwithmaths View Post
    Hi There,

    I've just been handed an assignment that I have no clue how to do..

    I will show you some of the questions below but I am not looking for straight answers. I would like some pointers on how to go about solving these where to get help.

    Introduction
    Show if the folowing statements are true or false for 2 x 2 matrices.

    1)
    det(AB) = det(A)det(B)
    2)
    det(A^-1)= 1(over)det(A)
    3)
    det(A^T)=det(A)

    Any advice would be greatly appreciated as this is due in one week and I have no clue how to go about this?

    Thanks..
    Define

    A = \left[\begin{matrix}a_{11} & a_{12} \\ a_{21} & a_{22}\end{matrix}\right] and B = \left[\begin{matrix}b_{11} & b_{12}\\b_{21} & b_{22}\end{matrix}\right]

    Find AB, A^{-1}\textrm{ and }A^T and then you can find the appropriate determinants and see if your statements hold true.
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