1. The problem statement, all variables and given/known data Let T be a linear transformation that maps Rn onto Rn. Show that T-1 exists and maps Rn onto Rn. Is T-1 also one to one? 2. Relevant equations 3. The attempt at a solution I am not quite sure where to start. To prove that T is invertible I need to show that A is an invertible matrix. To show that A is an invertible matrix I can use The Invertible Matrix Theorem part i. "The linear transformation x → Ax maps Rn onto Rn This theorem also says that if part i. is true then A is an invertible matrix. Then, by theorem 9, T is invertible because A is invertible. Is that enough to prove that T-1 exists? How do I show that it maps Rn onto Rn? Is it also 1-1?