# AB=0 but A and B different from 0

1. Sep 29, 2015

### bonildo

1. The problem statement, all variables and given/known data
Need to show that if A is not invertible then exist B (nxn) such that AB=0 but B is different from 0.

2. Relevant equations

3. The attempt at a solution
Thought about writing A like E1...Ek*R where Ei are elementary matrices and R(different from I) the row reduced echelon matrice but doesnt seem.to help, any idea??

2. Sep 29, 2015

### micromass

Staff Emeritus
Hint: a nontrivial linear combination of the columns/rows of $A$ is zero.

3. Sep 29, 2015

### WWGD

Similar to Micromass, write the columns so that they are in the " necessary ( and non-trivial) " kernel.