Finding a basis for an input matrix

Super lost on this homework assignment. The goal is to find a matrix, thought to be a collection of vectors, the columns of which form a basis of a given input matrix. My main idea is to take the rref of the input matrix, identify which columns include ones which are the first nonzero entry of their respective rows, and create a new matrix solely of the original columns which in the rref form had leading ones. It's similar to the approach presented here: https://www.math.ucdavis.edu/~daddel/Math22al_S02/LABS/LAB7/lab7_Winter06/node14.html

This seems to me to be the most straightforward way of generating a basis matrix but I cannot express how clueless I am. I don't even know where to begin. Please lend a hand!!