Modus ponens, that is [(A→B) and A, therefore B], is a valid argument.
If we use the form (1) [(A→B) and B, therefore A], the argument is no longer valid because for the assignment [A = False, B = True], we have the premises (A→B) and B both true but the conclusion A false.
It is said that propositional logic must hold only for the form of the arguments, not for the meaning of the propositions.
But try using A = "Today is Saturday", B = "Tomorrow is Sunday".
The assignment [A = False, B = True], which makes the argument invalid, is not possible, because A and B can only be both true or both false.
So argument (1) becomes valid? It seems like a small question but if you think about it, it is fundamental.
Best Answer
The validity of an argument gauges not the truth of the conclusion, but whether a false conclusion can result from premises that are all true. If yes, the argument is deemed invalid; otherwise—since there is no case whereby all the premises are true yet the conclusion is false—its corresponding conditional must be logically valid (in propositional calculus, this means a tautology).
Argument (1)—its form is called “affirming the consequent”—is invalid, because its corresponding conditional $((A\rightarrow B)\land B)\rightarrow A$ is not a tautology, since it is false for $A$ False and $B$ True.
The fact that when $A$ and $B$ are “Today is Saturday” and “Tomorrow is Sunday”, respectively, the conditional $((A\rightarrow B)\land B)\rightarrow A$ is true (weaker than tautologically true, i.e., true regardless of interpretation of $A$ and $B$) is just a peculiarity of this tautologically-equivalent choice of $A$ and $B.$ However, this doesn't affect argument (1)'s validity, which, as you correctly observe, depends on its form, not its atomic propositions' meanings.