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Problem
Problem
Let
A
A
A
and
B
B
B
be
3
×
3
3 \times 3
3
×
3
matrices of real numbers, where
A
A
A
is symmetric,
B
B
B
is skew-symmetric and
(
A
+
B
)
(
A
−
B
)
=
(
A
−
B
)
(
A
+
B
)
(A + B)(A - B) = (A - B)(A + B)
(
A
+
B
)
(
A
−
B
)
=
(
A
−
B
)
(
A
+
B
)
. If
(
A
B
)
t
=
(
−
1
)
k
A
B
(AB)^t = (-1)^k AB
(
A
B
)
t
=
(
−
1
)
k
A
B
, where
(
A
B
)
t
(AB)^t
(
A
B
)
t
is the transpose of matrix
A
B
AB
A
B
, find the value of
k
k
k
. a. 0 b. 1 c. 2 d. 3
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