Thread: Proof isomorphism

Hi so I was given a packet of proofs, I should solve and know and understand as a pre-req for Linear Algebra 2
But I got stuck on this one, I even read the section of the text that I have on isomorphism and still can't do this one.



I would really appreciate the Help

(a) prove the identity map is an isomorphism (i.e., that it's linear and bijective).
(b) isomorphisms are bijective. bijective maps have inverses. prove if a linear map T has an inverse T^-1, that T^-1 is linear.
(c) prove that the composition of two linear isomorphisms is again a linear isomorphism.

let me know if you have trouble with these.

I just went over all the material I am supposed to know, and I don't see a single thing about "identity map" or "bijective" or even just "map"

is there any other way to prove it

thank you

what is your definition of isomorphism?