Matrices

I do remember learning matrices in math class, but I do not remember how to solve them. All I remember is that they were frustrating because I had to follow all sorts of specific sets of rules, which varied depending on whether you were multiplying or adding the matrix, etc., that somehow led me to some unjustifiable answer.
Also, I think the caption beside the matrix at the left is quite comical, because this is exactly how I was taught matrices. "Just memorize the rules; they're special." No telling you this is why . . . and therefore I have forgotten.