Proving X is Full Column Rank Matrix if X^TX is Non-Singular

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Homework Statement

Show (in complete detail) that X is a full column rank matrix if and only if
X^TX is non-singular (invertible). Assume X is a real matrix.

X^T is X transpose

Homework Equations

The Attempt at a Solution

 

[Defennder]

What does the fact that X is of full rank imply about X? Secondly what does the fact that (X^TX) being invertible imply about what the previous statement concludes?

 

[Dick]

Show an attempt at solving the problem, please? Or at least say why you can't.