could some one please help me with proving this statement ab

could some one please help me with proving this statement |ab|=|a||b| and the profe has to be in cases

Solution

Answer :

Case I: when both a,b are positive

|ab| = ab = |a|*|b|

Case II: when both a,b negative

|ab| = ab = (-a)*(-b) = |a|*|b|

Case III: one negative, one positive

Assume a is positive, b is negative (since a,b are symmetrical, we can switch them as necessary)

|ab| = -ab = a*(-b) = |a|*|b|

Hence, in all the cases , we have |ab|=|a||b|