I apologize in advance for my inability to type out matrices. Anyway the

The linear transformation is T [x] [z]

[y] = [x]

[z] [y]

and the question states find T^2013. I'm sorry but I have no idea how we are supposed to solve this, short of taking an eternity to apply it 2013 times. Is there some sort of pattern that will be apparent? I'm just not seeing it, Thank you very much