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Let and be square matrices of real numbers
MATHEMATICS · Multi correct · CBSE · Mathematics · Matrices · Matrices
Problem
Let
A
A
A
and
B
B
B
be square 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)^kAB
(
A
B
)
T
=
(
−
1
)
k
A
B
, find the possible values of
k
k
k
. (1)
0
0
0
(2)
1
1
1
(3)
2
2
2
(4)
3
3
3
Related theory
Matrices
Symmetric and Skew-Symmetric Matrices
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