Determine the $n$-th power of matrix Determine the $n$-th power of the matrix. $$\pmatrix{2 & 2 & 0 \\ 1 & 2 & 1 \\1 & 2 & 1  \\ }$$ May you help me with the answer since the book states :  $${1\over 6}\pmatrix{4+2\cdot4^n & 3\cdot4^n & -4+4^n \\ -2+2\cdot4^n& 3\cdot4^n & 2+4^n\\-2+2\cdot4^n &  3\cdot4^n & 2+4^n  \\ }$$ while mine misses the ${1\over 6}$. So who is right?
$$$$Thanks in advance for any help you are able to provide.

I think about  $$\pmatrix{\left(2^{2n-1}-\frac{2}{3}(4^n-1)\right) & 2^{2n-1} & \frac{2}{3}(4^n-1) \\ \left(2^{2n-1}-\frac{2}{3}(4^n-1)+1\right) & 2^{2n-1} & \frac{2}{3}(4^n-1)+1 \\\left(2^{2n-1}-\frac{2}{3}(4^n-1)+1\right) & 2^{2n-1} & \frac{2}{3}(4^n-1)+1  \\ }$$ 
