Cube of a 2x2 Matrix

Find the cube of the matrix A =[[1,1],[1,0]]

[thomasolson]

Fibonacci matrix. I like to think of them as quadratic matracies because of the characterization polynomial is the quadratic.
Q:= (a, b, c) -> [[b/a, -c/a], [1, 0]], I need to double check this. You can multiply them by the powers Q^n to find trig stuff. I can't remember offhand what the function is in terms of e for the solutions.
There is also the rotation matrix [[x, y], [[-y, x]] and one for hyperbolic geometry that I know nothing about so far [[x, y], [y, x]].
I'm still messing with R3. I found some interesting ones with trig. I think there is more. I just barely scratched the surface.
I suspect that all of this stuff can be used in Mandelbrot Sets.

[billylee]

I got the foil when simplifying the constant (1/2 + sqroot of 5/2) but how did you do the shortcut method. I saw you just thought of some numbers to simplify the terms.

[martyfoster]

what do you do if lambda is a double root (lambda^2 -25 =0 or something like that)