Question

Prove that $(-1)\times (-1)=1$

Answer 1

Since 1 is the multiplicative identity, we know that $1\times (-1)=-1$. Using distributive property,
$0=(1-1)\times (-1)=1\times (-1)+(-1)\times (-1)$.
Thus $(-1)\times (-1)+(-1)=0$. Adding 1 both sides, we get
$(-1)\times (-1)=1$