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Byju's Answer
Standard XII
Mathematics
Skew Symmetric Matrix
Check whether...
Question
Check whether the given matric is symmetric or skew-symmetric.
A
=
⎡
⎢
⎣
1
2
−
5
2
−
3
4
−
5
4
9
⎤
⎥
⎦
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Solution
A
=
⎡
⎢
⎣
1
2
−
5
2
−
3
4
−
5
4
9
⎤
⎥
⎦
A
T
=
⎡
⎢
⎣
1
2
−
5
2
−
3
4
−
5
4
9
⎤
⎥
⎦
=
A
Since
A
=
A
T
, the given matrix is a symmetric matrix.
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Similar questions
Q.
If A and B are symmetric matrices of the same order, write whether AB − BA is symmetric or skew-symmetric or neither of the two.
Q.
If
B
is skew symmetric matrix write whether the matrix
(
A
B
A
T
)
is symmetric or skew symmetric.
Q.
If B is a skew-symmetric matrix, write whether the matrix AB A
T
is symmetric or skew-symmetric.
Q.
For
3
×
3
matrices
M
and
N
, which of
the following statement(s) is (are)
N
O
T
correct?
I
N
T
M
N
is symmetric or skew-symmetric, according as
M
is symmetric or skew-symmetric
I
I
M
N
−
N
M
is skew-symmetric for all symmetric matrices
M
and
N
I
I
I
M
N
is symmetric for all symmetric matrices
M
and
N
I
V
(
a
d
j
M
)
(
a
d
j
N
)
=
a
d
j
(
M
N
)
for all invertible matrices
M
&
N
Q.
If A is a skew-symmetric matrix and n is an even natural number, write whether A
n
is symmetric or skew-symmetric or neither of these two.
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