Hi, I've a problem with a (I know it must be very easy but I don't get it) demonstration about matrices...

The thing I've to show is...

Let A be a square matrix such as for all B (With the same order as A) AB=0. Then A=0.

I don't wanna prove that there are no zero divisors in this ring (Because there are)...just that there isn't a zero divisor A in this ring that AB=0 for ALL B and the only matrix that does that is the zero matrix of that order...this is what i mean...

--------------------------------------------------------

Sorry, Problem solved...It was truly a very simple (Trivial) demonstration...