A^2 =
-2 -2√3
2√3 2
A^3 = AA^2 =
-8 0
0 -8
= -8E.
所以
当n = 3k 时,A^n = (A^3)^k = (-8E)^k = (-8)^kE
当n = 3k+1 时,A^n = A(A^3)^k = A(-8E)^k = (-8)^kA
当n = 3k+2 时,A^n = A^2(A^3)^k = A^2(-8E)^k = (-8)^kA^2 = (-8)^k *
-2 -2√3
2√3 2