Suppose that A is a square. Show that A is invertible if and only if A^T*A is invertible.(adsbygoogle = window.adsbygoogle || []).push({});

I know that if A is an m X n matrix, m>=n, and rkA=n, then the n X n matrix A^T*A is invertible, and that rk(A^TA)= rkA, but I'm still not sure how to start the proof...

TIA

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