TITLE: Why minus times minus needs to be plus?
QUESTION [7 upvotes]: Possible Duplicate:
Why negative times negative = positive? 

An Abstract Algebra text book has a sentence on its 1st chapter about natural numbers that i cannot get around easily. The sentence reads "Why minus multiplied by minus needs to be plus is something you might reflect on now." I cannot answer the question, why minus multiplied by minus needs to be plus?
thanks

REPLY [4 votes]: Hint $\rm\ xy,\ (-x)(-y)\ $ are both inverses of $\rm\ x(-y)\ $ so they're equal by uniqueness of inverses.
As I often emphasize, uniqueness theorems provide powerful tools for proving equalities.