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multiplying a 3 by 2 with a 2 by 3 will result in a 3 by 3 the inner numbers have to match then the dimensions of the product will be the exterior numbers there
wait, what do you mean 3 by 2 and 2 by 3?

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Other answers:

those are the dimensions of your matrices respectively
anyways to find the entries you do rows from the first matrix with columns of the second matrix
for example entry 1 will be 2(5)+0(0)
in general the first element in the product matrix would look like this \[\left[\begin{matrix}a_{11} & a_{12} \\ a_{21} & a_{22} \\ a_{31} & a_{32}\end{matrix}\right] \cdot \left[\begin{matrix}b_{11} & b_{12} & b_{13} \\ b_{21} & b_{22} & b_{23}\end{matrix}\right] \\ =\left[\begin{matrix}a_{11} \cdot b_{11}+a_{12} \cdot b_{21} & ? & ? \\ ? & ? & ? \\ ? & ? & ?\end{matrix}\right]\]
basically we did the dot product of and
to find the first entry that is
|dw:1438660253075:dw|
this is so confusing, omg.
lol
do u want a formula?
|dw:1438660316576:dw|
Oh, okay okay, I get it now! Thank you!
https://en.wikipedia.org/wiki/Matrix_multiplication just in case I don't really want to type it all out but wikepedia already did you can see they multiplied a 3 by 2 with a 2 by 3 here look under rectanglular matrices BA
Whats the formula @dan815 :)
already did a formula for a 3 by 2 with a 2 by 3 *
|dw:1438660749700:dw|

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