document.write( "Question 1062036: The answer given by one tutor doesn't match the answer found at the back of my textbook, so I'm reposting.
\n" ); document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #676795 by ikleyn(52803) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "1. Not necessary. \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "2. Not if A and B are linear operators.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "3. As a rule, NO.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "4. But since $\"R%5E3\"$ and $\"R%5E2\"$ have the same cardinality, there are (do exist) some maps A and B
\n" ); document.write( " (highly non-linear and highly non-continuous) that BA IS invertible.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );