AB=0 but A and B different from 0

[bonildo]

Homework Statement

Need to show that if A is not invertible then exist B (nxn) such that AB=0 but B is different from 0.

Homework Equations

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 doesn't seem.to help, any idea??

 

[micromass]

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

 

[WWGD]

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