N-th power of matrix Find the formula for the n-th power of this matrix.
$$
\pmatrix{1&1\\1&0}
$$
Well $f^2 = \pmatrix{2&1\\1&1}$ and $f^3 = \pmatrix{3&2\\2&1}$ and $f^4 = \pmatrix{5&3\\3&2}$
and $f^5 = \pmatrix{8&5\\5&3}$... 
I can't seem to find the pattern here. Would someone mind helping me

Hint: For $F = \pmatrix{1&1\\1&0}$, show (perhaps inductively) that
$$
F^n = F^{n-1} + F^{n-2}
$$
Inductive step:
$$
F^{n+1} = F \cdot F^n = F(F^{n-1} + F^{n-2}) = F^n + F^{n-1}
$$
For the base case, note that $F^0 = I$.
