SOLUTION: The answer given by one tutor doesn't match the answer found at the back of my textbook, so I'm reposting. Let A:{{{R^3 -> R^2}}} and B:{{{R^2 -> R^3}}}, so that BA:{{{R^3 -> R^3}

Algebra ->  College  -> Linear Algebra -> SOLUTION: The answer given by one tutor doesn't match the answer found at the back of my textbook, so I'm reposting. Let A:{{{R^3 -> R^2}}} and B:{{{R^2 -> R^3}}}, so that BA:{{{R^3 -> R^3}      Log On


   

Question 1062036: The answer given by one tutor doesn't match the answer found at the back of my textbook, so I'm reposting.
Let A:R%5E3+-%3E+R%5E2 and B:R%5E2+-%3E+R%5E3, so that BA:R%5E3+-%3E+R%5E3. Is BA an invertible map?
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
1.  Not necessary.

2.  Not if A and B are linear operators.

3.  As a rule, NO.

4.  But since R%5E3 and R%5E2 have the same cardinality, there are  (do exist)  some maps  A  and  B
     (highly non-linear and highly non-continuous)  that  BA   IS   invertible.