Linear Algebra Proof - Columns of Matrix Linearly Independent & Determinant

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How can I prove that if the columns of matrix A are linearly independent, then det(A) does NOT equal zero?

This is a question on my exam review and I have no idea how to go about proving this. Any help is much appreciated!

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This is your exam review, so you should really solve it yourself. Doing so will help you remember what's going on in the exam. I will give you some hints on how to go about proving this:

  1. Prove if $det(A)$ = $0$, then columns of $A$ are linearly dependent. (By going through the definition of $det(A)$)
  2. Based on contrapositive version of 1, if columns of $A$ are linearly independent, then $det(A)$ = $0$ is false.

Best of luck to your exam.