1. The problem statement, all variables and given/known data Let u_1...u_n be linearly independent column vectors in R^n and A an invertible n x n matrix. Prove that the vectors Au_1...Au_n are linearly independent. 2. Relevant equations 3. The attempt at a solution It is easy to prove this using scalars and the definition of linear independence. But, then why is this relevant to invertible matrices? Is there a way to prove this using column spaces, row spaces, null spaces, etc?