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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 multiplicationThis question was posed to me at a job interview.My question is based upon Groups in chapter Groups of Discrete Mathematics

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.



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