O(1) Matrix Rotation. I think.

matrix.lua

local rawget = rawget
local rawset = rawset
local setmetatable = setmetatable
local tostring = tostring
local error = error
local type = type
local print = print

module("matrix")

local InternalMeta = {}
function InternalMeta:__index(key)
  if type(key) ~= "number" then return rawget(self.matrix[self.selection], key) end

	local mat = self.matrix
	local x,y = self.selection, key
	
	return mat(x, y)
end

function InternalMeta:__newindex(key, val)
	if type(key) ~= "number" then rawset(self.matrix[self.selection], key, val) end
	
	local mat = self.matrix
	local x,y = self.selection, key
	
	return mat(x, y, val)
end


local Matrix = {}

function Matrix:__index(key)
	if type(key) ~= "number" then return (rawget(self, key) or Matrix[key]) end
	
	local metahack = {}
	metahack.selection = key
	metahack.matrix = self
	return setmetatable(metahack, InternalMeta)
end

function Matrix:__call(x, y, ...)
	if x<=0 or y<=0 or x>self.size or y>self.size then error("Matrix index out of bounds") end

	local val = {...} --Just some trickery to make it so you can put multiple things in the same position in the matrix
	if val and #val == 0 then val = nil end
	if val and #val == 1 then val = val[1] end
	
	if val then --Set
		if self.rotation==0 then --Read normally
			self.internal[x][y] = val
		elseif self.rotation==1 then --Rotated once to the right
			self.internal[self.size-y+1][x] = val
		elseif self.rotation==2 then --Rotated 180 degrees from original
			self.internal[self.size-x+1][self.size-y+1] = val
		elseif self.rotation==3 then --Rotated once to the left
			self.internal[y][self.size-x+1] = val
		else
			error("Matrix has an invalid rotation number")
		end
	else --Get
		if self.rotation==0 then --Read normally
			return self.internal[x][y]
		elseif self.rotation==1 then --Rotated once to the right
			return self.internal[self.size-y+1][x]
		elseif self.rotation==2 then --Rotated 180 degrees from original
			return self.internal[self.size-x+1][self.size-y+1]
		elseif self.rotation==3 then --Rotated once to the left
			return self.internal[y][self.size-x+1]
		else
			error("Matrix has an invalid rotation number")
		end
	end
end

function Matrix:Zero(size)
	if size<1 then error("A Matrix was zeroed to a size of 0 or less.") end
	self.rotation = 0
	self.size = size or self.size
	self.internal = {}
	for i=1,size do
		local row = {}
		for j=1,size do
			row[j] = 0
		end
		self.internal[i] = row
	end
end

function Matrix:__tostring()
	local ret = ""
	for i=1,self.size do
		for j=1,self.size do
			ret = ret.."["..tostring(self(i, j)).."]"
		end
		ret = ret.."\n"
	end
	return ret
end

function Matrix:RotateLeft()
	self.rotation = (self.rotation-1)%4
end

function Matrix:RotateRight()
	self.rotation = (self.rotation+1)%4
end

return function(size)
	local m = {}
	m = setmetatable(m, Matrix)
	m:Zero(size or 1)
	return m
end