document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1062029>Question 1062029</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let A, B, and C be any nxn matrices.  Prove that trace(ABC) = trace(CAB) = trace(BCA). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #676783 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52787)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=676783\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Let A, B, and C be any nxn matrices.  Prove that trace(ABC) = trace(CAB) = trace(BCA).<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For it, it is enough to prove trace(AB) = Trace(BA).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For this, see\r<BR>\n" );
document.write( "\n" );
document.write( "<A  rel=nofollow HREF=http://math.stackexchange.com/questions/1099745/how-to-prove-tr-ab-tr-ba>http://math.stackexchange.com/questions/1099745/how-to-prove-tr-ab-tr-ba</A>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "http://math.stackexchange.com/questions/1099745/how-to-prove-tr-ab-tr-ba\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );