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Mathematics
Mathematics
Problem
Q1. Let
A
=
[
cos
θ
0
−
sin
θ
0
1
0
sin
θ
0
cos
θ
]
A = \begin{bmatrix} \cos \theta & 0 & -\sin \theta \\ 0 & 1 & 0 \\ \sin \theta & 0 & \cos \theta \end{bmatrix}
A
=
cos
θ
0
sin
θ
0
1
0
−
sin
θ
0
cos
θ
. If for some
θ
∈
(
0
,
π
)
\theta \in (0, \pi)
θ
∈
(
0
,
π
)
,
A
2
=
A
T
A^2 = A^T
A
2
=
A
T
, then the sum of the diagonal elements of the matrix
(
A
+
I
)
3
+
(
A
−
I
)
3
−
6
A
(A + I)^3 + (A - I)^3 - 6A
(
A
+
I
)
3
+
(
A
−
I
)
3
−
6
A
is equal to \_\_\_\_\_\_.
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