How to Prove Rank(A) Equals Rank(ATA)?

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Hi,

Does anyone know how to prove rank(A)=rank(AT A) where A is any matrix and AT is the transposed of matrix A? I have difficulty to prove the part that nulity(A)=nulity(AT A). Any help will be appreciated.
 
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Try proving \operatorname{ker} A = \operatorname{ker} ( A^\top A).
 

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