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Byju's Answer
Standard XII
Mathematics
Singular and Non Singular Matrices
A square matr...
Question
A square matrix
A
is skew-symmetric, such that
A
2
+
I
=
O
,
then
A
A
is orthogonal matrix
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B
A
is orthogonal matrix of odd order
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C
A
is orthogonal matrix of even order
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D
A
is involutry matrix
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Solution
The correct option is
C
A
is orthogonal matrix of even order
Given
A
is skew-symmetric matrix and
A
2
+
I
=
0
i
.
e
A
′
=
−
A
I
=
−
A
2
=
(
−
A
)
A
=
A
′
A
⇒
A
is orthogonal
Now
A
′
A
=
I
n
⇒
|
A
′
A
|
=
1
⇒
|
A
′
|
|
A
|
=
1
⇒
(
−
1
)
n
(
|
A
|
)
2
=
1
(
∵
(
|
−
A
|
)
=
(
−
1
)
n
|
A
|
)
∴
A
is an orthogonal matrix of even order.
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1
Similar questions
Q.
If
A
is a real skew-symmetric matrix such that
A
2
+
I
=
O
, then
Q.
A square matrix
A
is said to be orthogonal if
A
′
A
=
A
A
′
=
I
n
If
A
is real skew-symmetric matrix is such that
A
2
+
I
=
0
, then
Q.
If A = [a
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, then write whether A is symmetric or skew-symmetric.
Q.
If A = [a
ij
] is a square matrix of even order such that a
ij
= i
2
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, then
(a) A is a skew-symmetric matrix and | A | = 0
(b) A is symmetric matrix and | A | is a square
(c) A is symmetric matrix and | A | = 0
(d) none of these.
Q.
If A is a skew-symmetric matrix, then A
2
is a ___________ matrix.
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Standard XII Mathematics
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