ok ... i think i understand now.
as for the first question, yes they are the same. and as for the second, then they are different.
can someone plz clarify the following:
what is the difference between an invertible transformation, a bijective transformation and an isomorphism ? or are they all the same thing?
and furthermore, is there any difference between an invertible transformation and an inverse transformation?
For linear transformation, if a linear transformation is a "bijection" then it is invertible and is an isomorphism. That is not the case for non-linear transformations. Of course, in linear algebra, we are concerned only with "linearity" so we are always working with linear transformations.
The critical distinction is that "invertible" is an adjective while "inverse" is a noun!
If linear transformation, A, is "invertible", then there exist a linear transformation, B, such that AB= BA= the identity function. B is the "inverse" of A.