11 .
Let A be the set of all non-singular matrices over real numbers and let * be the matrix multiplication operator. Then

A. | < A, * > is a monoid but not a group |

B. | < A, * > is a group but not an abelian group |

C. | < A, * > is a semi group but not a monoid |

D. | A is closed under * but < A, * > is not a semi group |

12 .
Let (Z, *) be an algebraic structure, where Z is the set of integers and the operation * is defined by n * m = maximum (n, m). Which of the following statements is TRUE for (Z, *) ?

A. | (Z, *) is a group |

B. | (Z, *) is a monoid |

C. | (Z, *) is an abelian group |

D. | None of these |

13 .
Some group (G, 0) is known to be abelian. Then which one of the following is TRUE for G ?

A. | G is of finite order |

B. | g = g² for every g ∈ G |

C. | g = g-1 for every g ∈ G |

D. | (g o h)² = g²o h² for every g,h ∈ G |

14 .
If the binary operation * is deined on a set of ordered pairs of real numbers as (a,b)*(c,d)=(ad+bc,bd) and is associative, then (1, 2)*(3, 5)*(3, 4) equals

A. | (7,11) | B. | (23,11) |

C. | (32,40) | D. | (74,40) |

15 .
If A = (1, 2, 3, 4). Let ~= {(1, 2), (1, 3), (4, 2)}. Then ~ is

A. | reflexive | B. | transitive |

C. | symmetric | D. | not anti-symmetric |

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