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GATE20021.6
+9
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Which of the following is true?
The set of all rational negative numbers forms a group under multiplication.
The set of all nonsingular matrices forms a group under multiplication.
The set of all matrices forms a group under multiplication.
Both B and C are true.
gate2002
settheory&algebra
groups
normal
asked
Sep 15, 2014
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Set Theory & Algebra
by
Kathleen
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+1
How is B correct. Unless we fix the size of a nonsingular matrix to say n*n only then will the multiplication operator be closed. For a set of all non singular matrices, multiplication operator will not be even defined for some pairs.
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Answer: B
A: False. Multiplication of two negative rational numbers give positive number. So, closure property is not satisfied.
B: True. Matrices have to be nonsingular (determinant !=0) for the inverse to exist.
C: False. Singular matrices do not form a group under multiplication.
D. False as C is false.
answered
May 11, 2015
by
Rajarshi Sarkar
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Jun 2, 2015
by
Rajarshi Sarkar
comment
0
two non singular matrics multiplication is always nonsingular??
0
if $A$ and $B$ are nonsingular matrices, i.e. $det(A)$ $\neq$$0$ and $det(B)$ $\neq$$0$
then, $det(AB)$ =$det(A)$ $det(B)$ $\neq$$0$
so, $AB$ is also nonsingular always
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0
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Option b
answered
Feb 3, 2015
by
anshu
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C is false because singular matrices doesnot have inverse,
But why option A is wrong?
+6
Multiplication of two negative ll be a positive no.. so given set is not even closed.. thats why A is not a group..
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