We know that a compass points northward because Earth is a giant magnet. Does the northward-pointing needle point northward when the compass is brought to the Southern Hemisphere?

Yes

Explanation:

A compass needle always points in the north direction because the north pole of the magnet attracts the earth's magnetic north pole due to the presence of the earth's magnetic field. Earth itself is considered to be a large magnet. Due to this reason, every magnet used in the earth usually rests in the direction of the north pole.

It is a device that is used for the purpose of navigation but it does not always point towards the true north. The earth's magnetic north pole and the earth's geographical north pole are not the same. They are both different.

Thus, the compass having the needle pointing in the northward direction always points towards the north even if it is used in the southern hemisphere.

an angle + its complement = 90 degrees