# Property of determinants

1. Apr 14, 2012

### Hernaner28

Hi. I have the following sentence:

$$\begin{array}{l} A,B \in {M_{nxn}}\\ A \ne 0\\ B \ne 0\\ {\rm{if }}AB = 0{\rm{ then}}\\ {\rm{|A| = 0 or |B| = 0}} \end{array}$$

I know this is true but how can I realize? Just thinking about an example?

Thanks!

2. Apr 14, 2012

### morphism

Can you express the determinant of AB in terms of those of A and B?

3. Apr 14, 2012

### Ray Vickson

Do you know the relationship between $\det(A), \det(B) \text{ and } \det(AB)?$

RGV

4. Apr 14, 2012

### Hernaner28

Oh yes, it was incredibly simple: det(A)det(B)=det(AB) so det(A)det(B)=det(0) . I did one like this for symetric ones and I just didn't realize I could do the same here!
Thank you guys!

edit. What's RGV?

5. Apr 14, 2012

### Ray Vickson

It's a signature, the equivalent of "10-4 Good Buddy" or "over and out".

RGV