SOLUTION: Prove that if f : A → B is a function from A to B, then f ◦ iA = f and iB ◦ f = f. (iA: inverse of A).

Question 1179552: Prove that if f : A → B is a function from A to B, then f ◦ iA = f and iB ◦ f = f.
(iA: inverse of A).
Answer by ikleyn(52780)   (Show Source): You can put this solution on YOUR website!
.
Prove that if f : A → B is a function from A to B, then f ◦ iA = f and iB ◦ f = f.
(iA: inverse of A).
~~~~~~~~~~~~~~~~~~~~~~~~~~~

Then (f o iA) is identical map of the image of A (which is part of B) to B.

It is NOT TRUE that   (f o iA) = f,   as you write in your post.

Also, then (iA o f) is identical map of A to A.

It is NOT TRUE that   (iB o f) = f, as you write in your post.

Also, notice that " iB " is not defined in this problem and in this post, at all.

" iB " is totally fictitious subject, irrelevant to this problem.

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Where, from which source, did you retrieve these incorrect statements ?

Do you create / compose / invent them on your own ?

If you retrieve it from some source, then keep in mind that this source is UNTRUSTED.

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Notice that in this my post, I make not only my work as a tutor.

I make your part of work, too (also), trying to formulate the problem CORRECTLY.

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And the final note.

Everything what I wrote above, is written under the assumption that   iA is the inverse of A, as it is stated in your post.

I think that it is the key error in your post.

        If to assume that iA is IDENTICAL map of A to itself,
        and if to assume that iB is IDENTICAL map of B to itself,
        then all statements in your post become a)   correct and b)   self-evident.

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