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Math Help - General Linear Group Proof Help

  1. #1
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    General Linear Group Proof Help

    Let
    A Mn(F).
    Prove that A GLn(F) if and only if the columns of A form a basis for Fn.

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  2. #2
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    GL_n(F) is the group of invertible n by n matrices on F. The columns of a matrix span the image of the matrix in F^n. If those columns form a basis for F^n, then the image is the entire space and so the matrix is invertible.
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