Answer:
Explanation:
Matrix multiplication is really composition of functions, in particular, composition of linear transformations. It is usually the case that composition of functions is not commutative. For a standard example, consider the operation of putting on your shoes and the operation of putting on your socks. If you first put on your socks then put on your shoes, you get the desired result. If you first put on your shoes, then put on your socks, you get a different result. For an example with matrices, the matrix: A=[100−1] is a reflection across a horizontal line, namely the x-axis; while the matrix: B=[0110] is the reflection across the diagonal line y=x. You can verify that the matrix product AB does not equal the matrix product BA. That corresponds to composing the two reflections in different orders. The two compositions are two different rotations.