Let A, B be n-by-n matrices, w/ AB singular. Prove that....

[mammothrob]

Im stuck on this proof.

Let A and B be nxn matricies such that AB is singular. Prove that either A or B is singular.

Sooooo, here we go.

Let M = AB where is M is the given singular matrix.

Becuase M is singular then

Mx=0 has an infinite amount of solutions.

Let J be one of the non zero solutions

Mj=0

ABj=0

this is where I get stuck.
If knew that B was singular I think I could prove M is singular but Im having trouble from this way around.
Any ideas?

 

[pka]

If neither A nor B is singular, then AB is not singular.