document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=807873>Question 807873</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove or disprove the following for all 2x2 matrices A and B\r<BR>\n" );
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document.write( "1) (A + B)^2 = A^2 + 2AB + B^2<BR>\n" );
document.write( "2) A(A+B) = A^2 + AB\r<BR>\n" );
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document.write( "I have a hard time understand proofs and its due next week. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #486601 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=486601\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) (A + B)^2 = A^2 + 2AB + B^2\r<BR>\n" );
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document.write( "(A + B)^2 = (A+B)(A+B)\r<BR>\n" );
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document.write( "(A + B)^2 = A(A+B) + B(A+B)\r<BR>\n" );
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document.write( "(A + B)^2 = A*A+A*B + B*A+B*B\r<BR>\n" );
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document.write( "(A + B)^2 = A^2+A*B + B*A+B^2\r<BR>\n" );
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document.write( "This as far as we can go. We CANNOT say that A*B = B*A since matrix multiplication is NOT commutative in general.\r<BR>\n" );
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document.write( "Therefore (A + B)^2 = A^2 + 2AB + B^2 is false.\r<BR>\n" );
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document.write( "2) A(A+B) = A^2 + AB \r<BR>\n" );
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document.write( "A(A+B) = A*A + A*B\r<BR>\n" );
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document.write( "A(A+B) = A^2 + AB\r<BR>\n" );
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document.write( "So that confirms A(A+B) = A^2 + AB to be true. </SPAN>\n" );
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