1. Let U,V be finite dimensional vector spaces,with bases B,C respectively.

Prove:a linear map f:U->V is an isomorphism iff [f]_C^B is invertible.(I'm so sorry but I honestly couldn't get Latex to work properly,slightest change to "[f]" and it would cause an unknown latex error)

2. Let T:M_n(R)->T:M_n(R),T(A)=AC,C$\displaystyle \in$ M_n(R).

Prove that it is an isomorphism iff C is invertible.

Again so sorry for the inconvenience and any help would be appreciated.

Thanks in advance