If the matrix $$A = \left[ {\matrix{ 2 & 0 & 0 \cr 0 & 2 & 0 \cr 2 & 0 & 2 \cr } } \right]$$, then $${A^n} = \left[ {\matrix{ a & 0 & 0 \cr 0 & a & 0 \cr b & 0 & a \cr } } \right],n \in N$$, where