Suppose you have two matrices A and B. Let A be a 3x3 matrix and B be a 1x3 matrix.
As stated above, you can only multiply matrix C (mxn) by matrix D (pxq) if n=p. That is, the number of columns in C = the number of rows in D.
We see that for your problem, we have the following information,
$m=n=q=3$ and $p=1$.
Thus we have that $ n \neq p$.
If you insist on multiplying these two matrices together, you could always take the transpose of matrix B, denoted $B^{T}$. (For information about transposed matrices, see [1].)
$B^{T}$ would be a 3x1 matrix. So you could in fact do $AB^{T}$.
For more on matrix multiplication in general, see [2]. I hope this is helpful!
[1] Weisstein, Eric W. "Transpose." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Transpose.html
[2] Weisstein, Eric W. "Matrix Multiplication." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/MatrixMultiplication.html