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A matrix A is both symmetric and skew symmetric if A is
Null matrix
unit matrix
row matrix
none of these
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(A')'=
-A'
-A
A
A'
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(kA)'= (where k is any scalar)
-kA
kA'
-kA'
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(-A)'=
A'
-A'
-a
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(A+B)'=
A'-B'
A+B
B'-A'
A'+B'
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(AB)'=
A'B'
B'A'
BA
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A square matrix is known as symmetric matrix if
A+A'=0
A=A'
None of these
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Square matrix B is known as skew symmetric if
B=B'
B'+B=0
B-B'=0
none of these
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Every square matrix can be uniquely expressed as sum of a symmetric and skew symmetric matrix.
True
False
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For a square matrix A , A+A' is always a
Symmetric matrix
Skew Symmetric matrix
May be symmetric or may be skew symmetric
Can't say .
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For a square Matrix A, A-A' is always a
Symmetric Matrix
Skew Symmetric Matrix
Null matrix
None of the above
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Diagonal elements of a skew symmetric matrix are all zero
True
False
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If all diagonal elements of a square matrix A are zero then
A is a symmetric matrix
A is a skew symmetric matrix
A may or may not be skew symmetric matrix
Never a skew symmetric matrix
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If A and B are square matrix of same order and B is a skew symmetric matrix then the matrix ABA' is
Not a square matrix
Symmetric matrix
Skew symmetric matrix
May be symmetric may be skew symmetric
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If A is a square matrix then AA'
Is not defined.
Is a skew symmetric matrix
Is a symmetric matrix
= -AA'
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If A and B are symmetric matrices of same order then
AB-BA is
Not defined
a skew symmetric matrix
a symmetric matrix
always a null matrix
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If A is a symmetric matrix then order of the A may be
1x3
4x1
3x3
Only Batra Sir knows
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If A and B are square matrices of same order then AB'-BA'
is a null matrix
is not defined
is a symmetric matrix
is skew symmetric matrix
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If a square matrix A is symmetric matrix then kA is (where k is some scalar)
a symmetric matrix.
a skew symmetric matrix.
Symmetric matrix if k is positive
symmetric if k is negative