See attached photo. I do not understand how to use the fact that the first function is an isomorphism to prove that the inverse is one-to-one, onto and has the homomorphic property 26. Recall that if f : A B is a one-to-one function mapping A onto B, then f-(b) is the unique a e A such thatf(a) = b. Prove that if o : S → S' is an isomorphism of (S, *) with (S', *'), then o- is an isomorphism of(S', *') with (S, *).

Since, is an isomorphism, it is one-one onto homomorphism. Hence, its inverse exists and is…

Answered: 26. Recall that if f : A B is a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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See attached photo. I do not understand how to use the fact that the first function is an isomorphism to prove that the inverse is one-to-one, onto and has the homomorphic property

26. Recall that if f : A B is a one-to-one function mapping A onto B, then f-(b) is the unique a e A such that
f(a) = b. Prove that if o : S → S' is an isomorphism of (S, *) with (S', *'), then o- is an isomorphism of
(S', *') with (S, *).

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