A^4a = A(A^3a)
= A(5Aa-3A^2a)
= 5A^2a-3A^3a
= 5A^2a-3(5Aa-3A^2a)
= 14A^2a-15Aa
(a,Aa,A^4a)=(a,Aa,A^2a)K
K =
1 0 0
0 1 -15
0 0 14
|K|=14≠0,所以K可逆
再由已知a,Aa,A^2a线性无关
所以 (a,Aa,A^2a) 可逆
故 (a,Aa,A^4a) 也可逆.