Dimensions of the Result

If two rectangular matrices are put in order so that the inner dimension is the same in each, then the matrices can be multiplied.

The result is (in general) a rectangular matrix:

A_R×N B_N×C = Z_R×C

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. If the inner dimension cannot be canceled, then the product cannot be formed.

Look at the following product. (For now, ignore how the elements were calculated.)

This is a 3×2 matrix times a 2×2 matrix. The result is a 3×2 matrix.