数据库切换期间的MySQL事务

Question

I am working with MySQL transactions and have a question.

Say I have started a transaction on a database A using:

$mysqli->begin_transaction(MYSQLI_TRANS_START_READ_ONLY);

where $mysqli is handle to my database A and I do some queries.

Now without reconnecting and commiting, I select another DB Database B using:

$mysqli->select_db("B");

Now, will the transactions which I started on database A still be effective even after switching the DB?

I want the transactions to commit only after I give $mysql->commit() and not when switching DBs.

And if there are any errors, will it rollback in DB A as well as DB B if the transactions were started with handle as DB A?

Thanks in advance