If either a or b or both are 0, we have |ab|= 0 and |a|*|b|=0
For any real number a and b non equal to 0, one of the 3 following cases are true:
i) both a and b are positive:
then |ab|=ab, |a|=a, |b|=b
ab=a*b
|ab|=|a|*|b|
ii) both a and b are negative:
then |a|=-a, |b|=-b
|ab|=ab, for example if a=-3, b=-7: |(-3)(-7)|=|21|=21=(-3)(-7)=a*b
so
ab=(-a)*(-b)
|ab|=|a|*|b|
iii) one of them is positive and the other negative.
In our case let a be positive, b negative:
|a|=a, |b|=-b,
and |ab|=-ab, for example if a=3, b=-4; |3*(-4)|=|-12|=12=3*(4)=a*(-b)
thus:
-ab= a*(-b)
|ab|= |a||b|.
In each possible case of the signs of a and b we get: |ab|= |a||b|.