part a of this question was to show that similar matrices have the same trace, which i was able to prove without much difficulty.

part b says, how would one define the trace of a linear operator T on a finite dimensional vector space? and how would one show that this definition is well-defined?

i dont get what the question means when it says show the definition is well-defined. only notion of well-defined i have is for a function where if a=b then f(a)=f(b) but i dont see how that would apply here. thanks for any inputs