How would you confirm that a colorless liquid given to you is pure water?
Measurement of properties like freezing point and boiling point would give you a quick, qualitative though likely correct, answer.  The simplest to do is the measurement of the liquid's freezing point.  

If you can, partially freeze your solution in a kitchen freezer, stir well, then measure the temperature while stirring.  Since the freezing point of water is relatively insensitive to atmospheric pressure, you don't have to worry about correcting for the elevation where you live.  This method is commonly used as a quick way to check the calibration of a thermometer.  Of course a measurement of ${0 ^oC}$ would mean that you likely have water.  If it doesn't freeze, assuming your freezer is cold enough to freeze water, then it's not water.  If this is what you observe, drop a small ice crystal or a grain of salt into the solution to initiate ice formation just to be sure it is not supercooled.  Also, if it doesn't freeze, measure the temperature of the solution to be sure it is at least several degrees below ${0 ^oC}$.

A shortcut, or as a further check, if you have plenty solution to spare you could take a portion and add enough crushed ice that it doesn't all melt upon stirring.  If you get the same value (${0 ^oC}$) as in the first experiment, you can be pretty confident that your solution is water.  If it were some mixture of solutions with a freezing point of ${0 ^oC}$ (unlikely), this test would give you a different measurement than in the first test due to either colligative properties if the amount of ice is small relative to the whole solution or by creating a new, bulk solution with a different melting point than the original solution.  

If both of these experiments give you the same result of ${0 ^oC}$, I'll bet my house that it's water.