I know that there are pairs of 2x2 matrices that generate a free group. https://projecteuclid.org/download/pdf_1/euclid.mmj/1028999969
My question is: Is there a way to construct a set of 3 or more matrices that generate a free group? Even if it involves increasing the dimensions of the matrices, or expanding to the complex plane.
Thanks!
Actually there's a much more general theorem: every finitely generated free group is a subgroup of the free group on two generators. So you can find a set of three matrices that generate a free group by taking appropriate products of the two you already have.