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}

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: and B:, so that BA:. Is BA an invertible map?
Answer by ikleyn(52803) (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 and have the same cardinality, there are (do exist) some maps A and B
(highly non-linear and highly non-continuous) that BA IS invertible.

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