Ask a Question

Which of the following statement is true? (a)The set of all rational negative numbers forms a group under multiplication

← Prev Question Next Question →
+1 vote
712 views
in Discrete Mathematics by (558k points)
Which of the following statement is true?

(a) The set of all rational negative numbers forms a group under multiplication

(b) The set of all matrices forms a group under multiplication

(c) The set of all non-singular matrices forms a group under multiplication

(d) The set of matrices forms a subgroup under multiplication

This question was posed to me at a job interview.

My question is based upon Groups in chapter Groups of Discrete Mathematics

1 Answer

+1 vote
by (1.4m points)
selected by
 
Best answer
The correct option is (c) The set of all non-singular matrices forms a group under multiplication

Easiest explanation: Since multiplication of two negative rational numbers gives a positive number. Hence, closure property is not satisfied. Singular matrices do not form a group under multiplication. Matrices have to be non-singular (determinant !=0) for the inverse to exist. Hence the set of all non-singular matrices forms a group under multiplication is a true option.

Related questions

Welcome to TalkJarvis QnA, a question-answer community website for the people by the people. On TalkJarvis QnA you can ask your doubts, curiosity, questions and whatever going in your mind either related to studies or others. Experts and people from different fields will answer.

Most popular tags

biology – class 12 biology – class 11 construction & building materials chemistry – class 12 electronic devices & circuits network theory data structures & algorithms ii cell biology ic engine insurance finance money computational fluid dynamics engineering physics i discrete mathematics chemistry – class 11 aerodynamics casting-forming-welding i engineering mathematics operating system casting-forming-welding ii engineering drawing mysql engineering geology digital circuits wireless mobile energy management electrical measurements digital communications cyber security analytical instrumentation embedded systems electric drives cytogenetics advanced machining computer fundamentals life sciences basic civil engineering iot design of electrical machines physics – class 12 applied chemistry dairy engineering basic chemical engineering cloud computing microprocessor bioinformatics aircraft design aircraft maintenance software engineering drug biotechnology digital signal processing biochemistry data structures & algorithms i automotive engine design avionics engineering material & metallurgy energy engineering cognitive radio unix electrical machines biomedical instrumentation object oriented programming electromagnetic theory power electronics analog communications bioprocess engineering civil engineering drawing engineering metrology physics – class 11 mathematics – class 12 engineering chemistry i basic electrical engineering unit processes mongodb signals and systems cryptograph & network security hadoop mathematics – class 11 engineering physics ii html control systems engineering mechanics antennas analog circuits computer network java sql server javascript concrete technology chemical process calculation artificial intelligence design of steel structures c++ database management computer architecture engineering chemistry ii corrosion engineering chemical technology dc machines
Powered by TalkJarvis
...