document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=578689>Question 578689</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How does one show that an operator is invertible? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #370718 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=370718\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How does one show that an operator is invertible?<BR>\n" );
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document.write( "Let's say \"a\" is your operator.<BR>\n" );
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document.write( "You want it to operate on \"b\"<BR>\n" );
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document.write( "It gives you \"c\" as a result.<BR>\n" );
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document.write( "Now assume you have an operator \"d\"<BR>\n" );
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document.write( "You want it to operate on \"c\" and it gives you \"a\".<BR>\n" );
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document.write( "Do you see that \"d\" has undone what \"b\" did?<BR>\n" );
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document.write( "That means \"b\" and \"d\" are inverse operators.<BR>\n" );
document.write( "It also shows that \"b\" is invertible: it can be undone.<BR>\n" );
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document.write( "Dressing and undressing are invertible.<BR>\n" );
document.write( "Eating is not invertible.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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