Proof of an expression involving absolute value

[mindauggas]

Homework Statement

Prove: |ab|=|a||b|. (Hint: Consider the cases separately for various signs of a and b.)

Homework Equations

I think it asks me to prove it only from the definition of absolute value (if it is possible).

The Attempt at a Solution

|ab|= \frac{(ab), if (ab)\geq0}{-(ab), if (ab)<0}

I do the same with |a||b| ... but does it constitute a proof?

I actually have no idea how to prove such a thing.

 

[mindauggas]

Sry for the interruption, i found the answers in this forum ...

 

[The1337gamer]

Could you say this:

abs(ab) = positive sqrt((ab)^2) = positive sqrt((a^2)(b^2)) = positive sqrt(a^2)*positive sqrt(b^2) = abs(a)*abs(b)

 

[Frogeyedpeas]

So you've got the problem solved or do you need more into it?

 

[mindauggas]

Yeah I found the proof in the other threads