We can define matrix multiplication in an "obvious" way. Meaning just multiply the corresponding components. But this type of multiplication is not very interesting. The matrix multiplication that is would turns out being more useful. The simplest application of matrix multiplication is that we can regard a system of equations as simply . Another application is that linear transformations from can be again regarded as matrix multiplication. In fact, any linear transformation between two vector spaces in general can be expressed as a matrix. All of these connections follow by the way we define multiplication.