Question 11334 – Operator
November 15, 2023Data-Structures
November 15, 2023GATE 2002
| Question 6 |
Which of the following is true?
| The set of all rational negative numbers forms a group under multiplication. | |
| The set of all non-singular matrices forms a group under multiplication. | |
| The set of all matrices forms a group under multiplication. | |
| Both B and C are true. |
Question 6 Explanation:
A group G should follow 4 properties:
a. Closure: result of a * b must be in group G.
b. There must be an identity element i.e. e * a = a * e = a
c. There must be an inverse element b for every element a such that a * b = b * a = e
d. Associativity i.e. (a * b) * c = a * (b * c)
Rational negative numbers don’t form a group under multiplication, as multiplying two negative numbers results into a positive number, so closure property is not satisfied.
Set of non-singular matrices forms a group under multiplication.
The set of all matrices doesn’t form a group under multiplication, since there may not be an inverse for a matrix (in particular, for singular matrices).
a. Closure: result of a * b must be in group G.
b. There must be an identity element i.e. e * a = a * e = a
c. There must be an inverse element b for every element a such that a * b = b * a = e
d. Associativity i.e. (a * b) * c = a * (b * c)
Rational negative numbers don’t form a group under multiplication, as multiplying two negative numbers results into a positive number, so closure property is not satisfied.
Set of non-singular matrices forms a group under multiplication.
The set of all matrices doesn’t form a group under multiplication, since there may not be an inverse for a matrix (in particular, for singular matrices).
Correct Answer: B
Question 6 Explanation:
A group G should follow 4 properties:
a. Closure: result of a * b must be in group G.
b. There must be an identity element i.e. e * a = a * e = a
c. There must be an inverse element b for every element a such that a * b = b * a = e
d. Associativity i.e. (a * b) * c = a * (b * c)
Rational negative numbers don’t form a group under multiplication, as multiplying two negative numbers results into a positive number, so closure property is not satisfied.
Set of non-singular matrices forms a group under multiplication.
The set of all matrices doesn’t form a group under multiplication, since there may not be an inverse for a matrix (in particular, for singular matrices).
a. Closure: result of a * b must be in group G.
b. There must be an identity element i.e. e * a = a * e = a
c. There must be an inverse element b for every element a such that a * b = b * a = e
d. Associativity i.e. (a * b) * c = a * (b * c)
Rational negative numbers don’t form a group under multiplication, as multiplying two negative numbers results into a positive number, so closure property is not satisfied.
Set of non-singular matrices forms a group under multiplication.
The set of all matrices doesn’t form a group under multiplication, since there may not be an inverse for a matrix (in particular, for singular matrices).
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