15
$\begingroup$

Possible Duplicate:
How to prove $\text{Rank}(AB)\leq \min(\text{Rank}(A), \text{Rank}(B))$?

If $A$ is an $m\times n$ matrix and $B$ is a $n \times r$ matrix, prove that the rank of matrix $AB$ is at most $\mathrm{rank}(A)$.

I asked a similar question earlier phrased incorrectly. The above is closer to the actual question generalised.

  • 1
    A duplicate (actually at least a triplicate!). Handled [here](http://math.stackexchange.com/q/978/11619) and [here](http://math.stackexchange.com/q/48989/11619)2012-09-07

3 Answers 3