Question 1062036
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1.  Not necessary. 


2.  Not if A and B are linear operators.


3.  As a rule, NO.


4.  But since {{{R^3}}} and {{{R^2}}} have the same cardinality, there are  (do exist)  some maps  A  and  B 
   &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(highly non-linear and highly non-continuous) &nbsp;that &nbsp;BA &nbsp;&nbsp;<U>IS</U> &nbsp;&nbsp;invertible.