In transaction theory, it's usually assumed that a transaction reads or writes a same data item at most once. So your schedule is not valid since the transaction 1 reads A twice.
Unfortunately, text books do not always make it very easy to find. Here are some quotes I can find.
Philip A. Bernstein, Vassos Hadzilacos, Nathan Goodman
"Concurrency Control and Recovery in Database Systems" P.21 Section 2.1
To keep this notation unambiguous, we assume that no transaction reads or writes a data item more than once.
Gerhard Weikum, Gottfried Vossen
"Transactional Information Systems: Theory, Algorithms, and the Practice of Concurrency Control and Recovery" P.47 Section 2.3
To exclude redundancies of this kind, we henceforth make the following assumptions:
in each transaction each data item is read or written at most once