# AX=0 for any column vector X and A is a square matrix, A must be zero matrix?

AA is a square matrix and A=ATA=A^T, suppose that AX=0AX=0 for any column vector XX, how to prove that AA must be a zero matrix?

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Hint: if e1e_1 is the column vector (10⋮0)\pmatrix{1 \\ 0 \\ \vdots \\ 0}, what is Ae1Ae_1?
– Bye_World
2 days ago

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