document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=621266>Question 621266</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Is the set {-1,0,1} closed under multiplication? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #390670 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=390670\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> YES:<BR>\n" );
document.write( "The multiplication table for that set (with multiplication defined as we know it) is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-2%2C7%2C-1%2C8%2C%0D%0Ared%28rectangle+%280%2C0%2C6%2C6%29%29%2C%0D%0Aline%28-1.5%2C2%2C6%2C2%29%2Cline%28-1.5%2C4%2C6%2C4%29%2C%0D%0Aline%28-1.5%2C6%2C0%2C6%29%2Cline%28-1.5%2C0%2C0%2C0%29%2C%0D%0Aline%282%2C7.5%2C2%2C0%29%2Cline%284%2C7.5%2C4%2C0%29%2C%0D%0Aline%286%2C7.5%2C6%2C6%29%2Cline%280%2C7.5%2C0%2C6%29%2C%0D%0Alocate%280.5%2C7%2C-1%29%2C+locate%282.8%2C7%2C0%29%2Clocate%284.8%2C7%2C1%29%2C%0D%0Alocate%28-1.3%2C5.3%2C-1%29%2Clocate%28-1%2C3.3%2C0%29%2Clocate%28-1%2C1.3%2C1%29%2C%0D%0Alocate%280.8%2C5.3%2C1%29%2Clocate%280.8%2C3.3%2C0%29%2Clocate%280.5%2C1.3%2C-1%29%2C%0D%0Alocate%282.8%2C5.3%2C0%29%2Clocate%282.8%2C3.3%2C0%29%2Clocate%282.8%2C1.3%2C0%29%2C%0D%0Alocate%284.5%2C5.3%2C-1%29%2Clocate%284.8%2C3.3%2C0%29%2Clocate%284.8%2C1.3%2C1%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Factors are at the top and on the left; products are at the corresponding column-row intersection inside the red square.<BR>\n" );
document.write( "As you see, the products include only elements of the set {-1, 0, 1} that you started with, so the set is closed under multiplication. </SPAN>\n" );
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