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?
This provides examples of the characteristics of a given mapping.