Question

How to prove that a linear transformation is an isomorphism?

Answer 1

My english vocab with this is not that great, hope this will make sense: You can prove that it's a monomorphism by looking at its kernel (or the nullspace of the matrix). If it equals 0, then it is a monomorphism. Second, you can see if it's a epimorphism by observing whether the image generates the whole space (for example if linear transformation A:U->V, then the Im(A) must equal V for it to be epimorphism.) A linear tranformation that is epi- and monomorphism is by definition an isomorphism.

Answer 2

by gp method