Prove from the definition of "linearly independent" that if ${\{v_1,v_2,...,v_n\}}$ is linearly independent and if A is an invertible $n x n$ matrix, then the set ${\{Av_1,Av_2,...,Av_n\}}$ is linearly independent.
I ran in to this problem in my textbook and I am having trouble understanding how to reach the answer. My initial thought is that is has something to do with the fact that for a matrix to be invertible it's determinant must be non-zero. But that seems to contradict the definition of linearly independent which states that the only scalars that make $c_1v_1+c_2v_2+...+c_nv_n=0$ true must be $c_1=c_2=...=c_n = 0$