Is it possible to multiply the following two matrices?
**A**_{R×N} **B**_{N×C}

Yes. The inner dimension "N" matches.

If two rectangular matrices are put in
order so that the inner dimension is the same in each,
then
the matrices are *conformant* and
can be multiplied.
The result is (in general) a rectangular matrix:

A_{R×N}B_{N×C}=D_{R×C}

Look at the dimensions in the following product (for now, ignore how the elements were calculated):

The the product **AB** (if it can be formed)
has the same number of rows as **A**
and the same number of columns as **B**.
You can think of this as "canceling" the inner
dimension.