Let V and W be vector spaces such that dimV=dimW, and let T:V->W be an isomorphism. Show that there exist bases B and C for V and W, respectively, such that [T]_(B)^(C) is a diagonal matrix__. What is the completion of the instruction?
A) with all diagonal elements being zero.
B) with all diagonal elements being ones.
C) with non-zero diagonal elements only.
D) with varying diagonal elements.