Why negative times negative is positive?

Question

I know that many people would say I don't even know this. But I know it very well that negative × neagtive = positive. But I don't know Why? So kindly give a logical answers.

Answer 1

Debt is negative. If you take away someones debt, you would be practically giving them positive money.

Answer 2

Mathematically, we define $\mathbb{R}$ to be an ordered field, which has this property (proposition 1.18 in baby Rudin). Intuitively, "negative"="opposite", and the opposite of the opposite is the same.