Determine if {v_{1},v_{2,}...v_{n}} is a basis ofRand A is invertible n x n matrix, then {Av^{n }_{1},Av_{2}...Av_{n}} is a basis ofR^{n}

So I got all the questions before this correct, but this one confusing me.

I'm not sure what a matrices invertibility has to do with any of this. I do know (i think I know) that if a matrix is invertible then it has linearly independent columns. It looks like {Av_{1},Av_{2}...Av_{n}} is supposed to be the basis of some matrix transformation but I'm lost on any of the rest of it.