I think there are two parts to matrix multiplications: 1) How you do it by hand, which this page offers a very handy and easy to remember recipe for. 2) And w

I think there are two parts to matrix multiplications: 1) How you do it by hand, which this page offers a very handy and easy to remember recipe for. 2) And why you do it in such a weird and not very multiplicative way. Matrix multiplication is so arbitrary when first introduced. Every time I see it work for some real life application I am surprised how mathematicians came up with it in the first place.