Matrix multiplication

[quasar987]

What was the (historical) motivation for defining the rules of matrix multiplication the way it is?

[masudr]

As far as I know, it comes from performing 2 linear transformations, A and B, one after the other. Then realising that both linear transformations can be written as one matrix, C, and then realising that C can be written as the A and B if we define this new operation called matrix multiplication.