I remember asking in freenode irc channel ##math that why matrix multiplication is defined like that, why not in any other way. I was told that:

>> cuz the composition of linear maps are defined like that.

It took a long time to understand what they meant. Still I see how it is taught to work out mechanically. Brave friends of mine went to the Wikipedia page to come back with more confusion. Wikipedia is a great reference when you know the subject well enough.

https://en.wikipedia.org/wiki/Wikipedia:WikiProject_Mathemat...