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Math Help - Inverse Matrices

  1. #1
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    Inverse Matrices

    I'm working through a tutorial on matrices: Pauls Online Notes : Linear Algebra - Finding Inverse Matrices

    I'm confused about the following bit:

    If A is invertible then there are a set of elementry matrices E_k...E_2E_1 such that E_k...E_2E_1A=I_n. If we multiply both sides of this by A^{-1}:

    E_k...E_2E_1AA^{-1}=I_nA^{-1}\Rightarrow A^{-1}=E_k...E_2E_1I_n

    I'm confused by that statement. I don't see how to get to isolate the inverse to obtain A^{-1}=E_k...E_2E_1I_n. On the left side of the arrow, I have E_k...E_2E_1AA^{-1}=E_k...E_2E_1I=I_nA^{-1}, but I still don't see how this implies that A^{-1}=E_k...E_2E_1I_n
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  2. #2
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    Quote Originally Posted by adkinsjr View Post
    I'm working through a tutorial on matrices: Pauls Online Notes : Linear Algebra - Finding Inverse Matrices

    I'm confused about the following bit:

    If A is invertible then there are a set of elementry matrices E_k...E_2E_1 such that E_k...E_2E_1A=I_n. If we multiply both sides of this by A^{-1}:

    E_k...E_2E_1AA^{-1}=I_nA^{-1}\Rightarrow A^{-1}=E_k...E_2E_1I_n

    I'm confused by that statement. I don't see how to get to isolate the inverse to obtain A^{-1}=E_k...E_2E_1I_n. On the left side of the arrow, I have E_k...E_2E_1AA^{-1}=E_k...E_2E_1I=I_nA^{-1}, but I still don't see how this implies that A^{-1}=E_k...E_2E_1I_n


    For any square matrix K of order n, KI_n=I_nK=K

    Tonio
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  3. #3
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    Ok, I think I was confused by the notation. I forgot that I_n was just an nxn identity matrix. For some reason I thought it was an elementary matrix with 1 row op.
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