Order Matters:AB is not BA in Matrix Operations

Caution: order matters. AB is not BA

Note that AB and BA are not the same thing at all. From this interpretation, it is clear that the conversion of oranges to bananas is not the same as the conversion of carrots to oranges. The other hand–well, actually it may be worse than we thought. The thing may not even be well-defined. Cause if the width of A is equal to the height of B. then we can do this product.

But we don’t necessarily know that the width of B will equal the height of A. We would need to show that for that one. Be aware that the size condition to be able to do a product might not make sense. One of them might not seem to make sense, even though the other one does. They are usually completely different things. Although the two ideas may make sense individually, they often refer to two completely different concepts.

Note: AB/=BA!