Question

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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Transcribed Image Text

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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