When does Matrix Multiplication Exist?

I wanted to make the title: 'When is Matrix Multiplication Well-Defined', but the software wouldn't let me.

If we have two matrices $A$ and $B$, then $AB$ is well defined if and only if the number of columns of $A$ equals the number of rows of $B$.

Is this right?

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Yes, that’s exactly right. –  Brian M. Scott Dec 8 '12 at 23:10
Great, thanks a lot! –  matrix Dec 8 '12 at 23:12
My pleasure. $\,$ –  Brian M. Scott Dec 8 '12 at 23:13
If $A=(a_{ij})$ and $B=(b_{jk})$ are matrices, with $1\leq i\leq n$, $1\leq j\leq p$, $1\leq k\leq q$ then the product $C=AB=(c_{ik})$ is the $(n\times q)$-matrix define by $c_{ik}=\sum_{j=1}^{p}a_{ij}b_{jk}$.