Proof of an expression involving absolute value

1. Dec 17, 2011

mindauggas

1. The problem statement, all variables and given/known data

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

2. Relevant equations

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

3. 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.

Last edited: Dec 17, 2011
2. Dec 17, 2011

mindauggas

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

3. Dec 17, 2011

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)

4. Dec 17, 2011

Frogeyedpeas

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

5. Dec 17, 2011

mindauggas

Yeah I found the proof in the other threads