RR=R: Solving the Matrix Conundrum

[imsoconfused]

given R=[.5 .5]
_______[.5 .5]
(that's a two by two matrix where each term is .5)
why is RR=R?

I was just looking at the matrix and wondered what principle is behind that fact.

 

[Defennder]

I don't see any "principle" behind this. It is just matrix multiplication with the matrices involved given the values such that it holds. It's a little like asking why 32-16 = 16. (why is 16 still there? Didn't I subtract it from 32 just now?).

 

[imsoconfused]

well that's subtraction, which is kind of what I mean by principle. what I'm trying to do is find a way to express this in words... I can write out the equation until I'm blue in the face but that won't answer my question. are you saying that when you multiply any matrix times itself, you get that same matrix? I don't think that's true, but I could be missing something.