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[单选题]
设A、B均为n阶方阵,则下列命题中不正确的是()
A.A^kA^l=A^k+l
B.(A^k)^l=A^kl
C.(AB)^k=A^kB^k
D.(AB)^k=A(BA)^k-1B
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A.A^kA^l=A^k+l
B.(A^k)^l=A^kl
C.(AB)^k=A^kB^k
D.(AB)^k=A(BA)^k-1B
证明:设A,B都是n阶正交方阵,则
(1)|A|=1或-1(2)AT,A-1,AB也是正交方阵。
(2) A正交方阵,得ATA=E,由AAT=E得AT正交方阵。又A-1=AT, 故A-1正交方阵。A,B是n阶正交矩阵,故A-1=AT,B-1=BT。(AB)T(AB) =BTATAB=B-1A-1AB=E, 故AB也是正交方阵。