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    Characteristics of a mapping

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    Let M be a two by two matrix for which each element is a real number, and let S be the set of all such matrices. Consider the mapping f of S to the real numbers R defined by the relation f(M) = determinant of M.

    a. Is this mapping onto? Why or why not?
    b. Is this mapping one to one? Why or why not?
    c. Is this mapping a homeomorphism? Why or why not?
    d. Is this mapping an isomorphism? Why or why not?

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    Solution Summary

    This provides examples of the characteristics of a given mapping.