SOLUTION: Let A:{{{R^3 ->R^2}}} and B:{{{R^2 ->R^3}}}, so that BA:{{{R^3 ->R^3}}}. Is BA an invertible map?

Algebra ->  Matrices-and-determiminant -> SOLUTION: Let A:{{{R^3 ->R^2}}} and B:{{{R^2 ->R^3}}}, so that BA:{{{R^3 ->R^3}}}. Is BA an invertible map?      Log On


   

Question 1062034: Let A:R%5E3+-%3ER%5E2 and B:R%5E2+-%3ER%5E3, so that BA:R%5E3+-%3ER%5E3. Is BA an invertible map?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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1.  Not necessary.

2.  Not if A and B are linear operators.

3.  Not as a rule.

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