Sorry if this is the wrong section - there seems to be a few matrices questions in here though. The question goes:

Let A be the $\displaystyle 2\times2$ matrix given by

$\displaystyle A=\left( \begin{array}{cc} 0.8 & 0.2 \\ 0.2 & 0.8 \end{array} \right).$i)Find the eigenvalues and eigenvectors of the matrix A.

ii)Find an orthogonal matrix O, which diagonalizes A.

iii)Compute $\displaystyle A^{100}$.

I'm rubbish with stuff like this.