1. Create the arrays on the stack (including the 3x2 resulting matrix)
2. Read in the arrays (from file, console, etc)
3. For each row vector in the 3x3 matrix (first loop), and each column vector in the 3x2 matrix (second loop), compute the dot product. This is done by simply multiplying the corresponding components and adding those products together (third loop).
@benjelly: Actually you DO need 3 loops. Each element i,j of the product matrix is the scalar product of row * column. To do the scalar product, you need 1 loop, and 2 extra loops to run through each i,j element . :-)