Suppose that X is linearly dependent then show that (X^TX)^-1 does not exist…
This is updated in the exam. You can imagine that if X is not full thank then the square matrix composed of the column space of X would not actually exist. This is also why I have given the hint about proof by contradiction by assuming that X is dependent and trying to construct the square matrix which is still invertible (you will run into a contradiction).
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