If A is invertible then KerB=KerAB A is m _m matrix and B is a m_ n matrix. Show that if A is invertible then KerB=KerAB. I have been thinking that let x belongs to KerB so that Bx=0. A*A^-1*Bx=In*Bx=Bx but dont know how to continue.

You have chosen an arbitrary element $x \in \ker B$. You should prove that this element also lies in $\ker AB$, to show the inclusion $\ker B \subset \ker AB$. After that you'll also have to show the other inclusion, where you'll have to use the fact that $A$ is invertible.