Determinants : Proof det(AB)=0 where Amxn and Bnxm with m>n

[Javé]

Can someone help me?

I'm trying to proof this:

Proof det(AB)=0 where Amxn and Bnxm with m>n

I created a generic matrix A and B, then I use Laplace transforms to conclude.

I'd like to know if there is another way to proof that.

Thanks!

 

[Javé]

Let A be a m×n matrix and B be a n×m matrix. If n<m then AB is not invertible.

Can someone proof this?
Could anybody help me?

 

[Steven G]

I guess that you have two matrices and the determinant of their product is 0.

You want to know how to show that the product is 0? That is easy, compute the determinant.

Or are you saying that given any two matrices A and B of the size you mentioned then det(AB) is always 0?