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线性代数
题库 #8447
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题目
#8447
设
A
=
(
a
11
a
12
a
13
a
21
a
22
a
23
a
31
a
32
a
33
)
,
P
=
(
0
0
1
0
1
0
1
0
0
)
A = \left(\begin{array}{lll} {a}_{11} & {a}_{12} & {a}_{13} \\ {a}_{21} & {a}_{22} & {a}_{23} \\ {a}_{31} & {a}_{32} & {a}_{33} \end{array}\right),P = \left(\begin{array}{lll} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array}\right)
A
=
a
11
a
21
a
31
a
12
a
22
a
32
a
13
a
23
a
33
,
P
=
0
0
1
0
1
0
1
0
0
,且
P
n
A
P
m
=
A
{P}^{n}A{P}^{m} = A
P
n
A
P
m
=
A
,则正整数
n
,
m
n,m
n
,
m
可以为
‾
\underline{\qquad}
.
A.
n
=
m
=
4
n = m = 4
n
=
m
=
4
B.
n
=
5
,
m
=
4
n = 5,m = 4
n
=
5
,
m
=
4
C.
n
=
4
,
m
=
5
n = 4,m = 5
n
=
4
,
m
=
5
D.
n
=
m
=
5
n = m = 5
n
=
m
=
5
解析
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