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Byju's Answer
Standard XII
Mathematics
Skew Symmetric Matrix
For a matrix ...
Question
For a matrix
A
,
A
I
=
A
and
A
A
T
=
I
is true
A
If
A
is a square matrix
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B
If
A
is a non-singular matrix
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C
If
A
is a symmetric matrix
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D
If
A
is any matrix
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Solution
The correct option is
A
If
A
is a square matrix
F
o
r
a
m
a
t
r
i
x
A
,
A
I
=
A
,
A
A
T
=
I
T
h
e
n
,
A
i
s
s
q
u
a
r
e
m
a
t
r
i
x
.
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0
Similar questions
Q.
A
is a square matrix of order
n
.
ℓ
=
maximum number of distinct entries if
A
is a triangular matrix
m
=
maximum number of distinct entries if
A
is a diagonal matrix
p
=
minimum number of zeroes if
A
is a triangular matrix
If
ℓ
+
5
=
p
+
2
m
, find the order of the matrix.
Q.
A
is a square matrix of order
n
.
l
=
maximum number of distinct entries if
A
is a triangular matrix
m
=
maximum number of distinct entries if
A
is a diagonal matrix
p
=
minimum number of zeroes if
A
is a triangular matrix
If
l
+
5
=
p
+
2
m
, find the order of the matrix.
Q.
Lets
A
=
[
0
5
−
5
0
]
be a skew symmetric matrix and
I
+
A
is non singular, then the matrix
B
=
(
I
−
A
)
(
I
+
A
)
−
1
is
Q.
If
A
is a non singular matrix such that
A
A
T
=
A
T
A
=
I
, and
B
=
A
−
1
A
T
, then matrix
B
is
Q.
Assertion :If A is a non-singular symmetric matrix, then its inverse is also symmetric.
B
e
c
a
u
s
e
Reason:
(
A
−
1
)
T
=
(
A
T
)
−
1
, where A is a non-singular symmetric matrix.
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