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?

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Question 1062034: Let A: and B:, so that BA:. Is BA an invertible map?
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.
1.  Not necessary.

2.  Not if A and B are linear operators.

3.  Not as a rule.

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



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