Why does multiplying 2 negative numbers make a positive one?

Is it even logical?

\((-a) \times (-b) = +ab\)

You're right, why would 2 negative numbers make it positive?

Math is entirely the study of logical consistency. I'd like the explanation too

Negative times negative is positive is a forced logical consequence of these next two basic beliefs of arithmetic, that \(a×0=0\) and \(a(b+c)=ab+ac\). Here’s why:

We’ll prove \((−a)×(−b)=+ab\):

By the first of the rules we must say: \((−a)×0=0\).

By rewriting the first zero we must then agree that: \((−a)×[b+(−b)]=0\).

By distributing the \(a\) into the terms found inside \([...]\) we must also agree that:

\((−a)×b+(−a)×(−b)=0\)
\(−ab+(−a)×(−b)=0\)

Rearranging (i.e. taking the \(-ab\) over to the other side of the equation):

\((−a)×(−b)=+ab\)