Visit matrixmultiplication.xyz. This question bothered me a few times until I studied math in the university. There, I had in total four linear algebra courses, so matrix multiplication became my bread-and-butter. One day it just snapped in my mind how the number of rows of the first matrix has to match the number of columns in the second matrix, which means they must perfectly align when the second matrix is rotated by 90°. From there, the second matrix trickles down, "combing" the values in the first matrix. The values are multiplied and added together. In my head, I called this the "waterfall method", and used it to perform my calculations in the university courses. It worked.