## College Algebra (6th Edition)

To add two matrices, they must have the same order. To multiply two matrices, the first must have as many columns as the other has rows. So if A and B are both, say, 3$\times$2 matrices, they can be added (they have the same order) but they can not be multiplied (A has 2 columns, B has 3 rows...) It is possible, so it makes sense.