I'm trying to teach myself about ordinary differential equations with an old script and I'm struggling with this problem: 

Show that the matrix product is continuous with respect to
the matrix norm. That is, if $A\_j → A$ and $B\_j → B$ we have $A\_j\cdot B\_j → AB$.

My problem is that I don't even understand what the limit of $A\_j\cdot B\_j$ has to do with the matrix norm. 

Any help would be greatly appreciated!