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Math Help - Linear System

  1. #1
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    Linear System

    Suppose A is a square matrix and the homogeneous system (A^2)^T X = 0 has a unique solution.Can any conclusion be made on the linear system AX=0.
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  2. #2
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    Yes, AX=0 has unique solution

    Proof :
    rank(A)=rank(A^T) ref attachment
    n\geq rank(A)\geq rank(A^2)=rank((A^2)^T)=n\rightarrow rank(A)=n
    So AX=0\rightarrow X=A^{-1}0=0
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