Quick Linear Algebra-True or false type

[workerant]

Quick Linear Algebra---True or false type

Homework Statement

If A is a m*n matrix and B is a n*n matrix, does nullity AB= nullity A* nullity B?

I think that it does, but I am not sure. I don't need a proof of this or anything, this is just a fact I need to know in order to try and prove something more complicated.

 

[Office_Shredder]

Are you sure null(A)*null(B) is always small enough to be equal to null(AB)? Try, e.g. m=n=3 and see if you can get null(A)=null(B)=2

If you're stuck, check the spoiler

Spoiler

For an even more trivial case, m=n=2, A=B=0 the zero matrix.