document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=477607>Question 477607</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with those problems. Thanks a lot!!!<BR>\n" );
document.write( "Multiplication is commutative because x*y = y *x for all x and y. Multiplication is associative<BR>\n" );
document.write( "because x *(y *z) = (x *y) *z. The identity of multiplication is 1, because x*1 = x for all x.<BR>\n" );
document.write( "Let a & b = a + ab + b for all a and b.<BR>\n" );
document.write( "(a) Is the operation & commutative?<BR>\n" );
document.write( "(b) Is the operation & associative?<BR>\n" );
document.write( "(c) What number is the identity of &?<BR>\n" );
document.write( "(d) What number is the inverse of 3 with respect to &? (Recall that the inverse of 3 with<BR>\n" );
document.write( "respect to multiplication is 1/3 because 3 * 1/3 equals the identity of multiplication.)<BR>\n" );
document.write( "Thank you very much for your help!!!! I appreciate it a lot!!!!!!! Thanks!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #327314 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=327314\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a\ &\ b\ =\ a\ +\ ab\ +\ b\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ b\ &\ a\ =\ b\ +\ ba\ +\ a\">\r<BR>\n" );
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document.write( "Apply the commutative properties of Addition and Multiplication to the RHS of the second equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ b\ &\ a\ =\ a\ +\ ab\ +\ b\ =\ a\ &\ b\">\r<BR>\n" );
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document.write( "So, yes the operation \"<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE &\">\" is commutative <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \forall a,\,b\ \in\ \mathbb{R}\">\r<BR>\n" );
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document.write( "You only get one problem per post.  Send me a note and I'll give you a quote for the other three problems.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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