We don't like to do homework, but this sounds more like joining in an argument.
The answer depends a lot on what your teacher means by the word
'magnet'. I'm guessing she may mean 'something that keeps a big
magnetic field for a long time'. In other words, she may mean what's
called a permanent magnet. In that case, there will be strong forces
between the magnet and either another magnet or a piece of magnetic
material (like iron) which has not been made into a permanent magnet,
but only magnetizes when in a magnetic field from something else.
Unless you're careful, you may not notice the difference between
magnetic material and another permanent magnet. The other permanent
magnet could either repel or attract the first one, depending on how
you turn it. Non-magnetized magnetic material will always be attracted
to the magnet.
Of course, your teacher may have something else entirely in mind.
You can get the wrong answer if the thing you're testing isn't a
magnet but is an unmagnetized piece of iron, and your "something
magnetic put next to it" happens to be a permanent magnet.
One way to be sure that your test piece material isn't magnetic is
if it's a wire. Moving a permanent magnet around a loop of wire will
induce a voltage around that loop which can be read with a galvanometer
(or any sensitive voltmeter) -- this takes advantage of Faraday's law
A compass needle may also be handy, but as they are magnetized,
they will be affected, even if just a little bit, by an unmagnetized
piece of material (if for no other reason than that the unmagnetized
piece of material may distort the local magnetic field from the Earth.
Compasses are notoriously unrelaible on metal ships and inside cars
made of steel).
(published on 10/22/2007)