Ruby class for 2x2 matrices, plus a section that rotates around a grid

RubyRot.rb

# Our class
class Matrix2by2

	# Initialize with a 2x2 list
	def initialize(x, y)
		if not (x.is_a? Array and y.is_a? Array) then
			throw(:notArray)
		end
		if (x.length != 2 and y.length != 2) then
			throw(:notEqual)
		end
		@x = x
		@y = y
	end

	# Overload access operator
	def [](n)
		return @x if n == 0
		return @y if n == 1
		throw(:OutOfBounds!)
	end

	# Overload addition operator
	def +(a)
		@x[0] += a[0][0]
		@x[1] += a[0][1]
		@y[0] += a[1][0]
		@y[1] += a[1][1]
	end

	# Overload multiplicaiton operator
	def *(a)

		z = [Array.new(2), Array.new(2)]
		z[0][0] = @x[0]*a[0][0] + @x[1]*a[1][0]
		z[0][1] = @x[0]*a[0][1] + @x[1]*a[1][1]

		z[1][0] = @y[0]*a[0][0] + @y[1]*a[1][0]
		z[1][1] = @y[0]*a[0][1] + @y[1]*a[1][1]

		return Matrix2by2.new(z[0], z[1])
	end

	# Print matrix
	def printContents()
		puts("| #{@x[0]} #{@x[1]} |")
		puts("| #{@y[0]} #{@y[1]} |")
	end

	# Print matrix
	def printAsGrid(maxDim)
		midway = maxDim/2
		grid = Array.new(maxDim)

		0.upto maxDim-1 do |n|
			grid[n] = " "*79
		end

		0.upto maxDim-1 do |n|
			grid[n][midway] = "|"
			grid[midway][n] = "-"
		end
		grid[midway][midway] = " "

		grid[midway - @x[0]][midway + @x[1]] = "*"
		grid[midway - @y[0]][midway + @y[1]] = "*"

		for line in grid do
			puts line
		end
	end
end

#Make a new matrix
z = Matrix2by2.new([1, 5], [2, 8])


#double the matrix
z *= Matrix2by2.new([2,0],[0,2])

#print info
puts("The matrix we're going to rotate a whole 360 degrees" +
	 " in 15 degree steps:")
z.printContents


#converts degrees to radians
def degToRad(deg)
	return deg*Math.acos(-1)/180
end

#the variable named "deg" is such a lie
(0..360).step(15) do |n|
	deg = degToRad(n)

	(z * [[Math.cos(deg), -Math.sin(deg)],
		  [Math.sin(deg), Math.cos(deg)]]).printAsGrid(37) 
	puts("="*80)
end