Hi everyone, I was given a set of proofs that I must understand but the explanation I have found after much research is way to complicated for an into to linear Algebra course, it explains it for an Injection what I need is it proved for a 1-1, after reading online about injection I foudn its the same thing, but this proof mentions things like homomorphism which I have no clue what it is and not in curriculum

So Please if anyone can Please please explain this proof in simpler terms I would more then appreciate it!!!

so this is the question

This is what I Found online