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?
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?