How would multiplying money work? This is a very silly question since nobody will actually do this because it makes very little sense in the real world but I just want to know how would it actually work if possible.
For example let us take an amount of 2 dollars and 2 cents and multiply that buy 2 dollars and 2 cents. Would the result be 4 dollars and 4 cents? The only way to make sense out of this for me is to treat them as vectors and multiply components.

You'd just combine the cents and dollars into one dollar value: $\$2.02*\$2.02 = 2.02*2.02=4.0804$. I guess the units would be square dollars...
