document.write( "Question 1077157: If A and B are matrices conformable for the product AB , prove that (AB)' = B'A'. \n" ); document.write( "
Algebra.Com's Answer #691686 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "(AB)'(AB) = I\r\n" );
document.write( "\r\n" );
document.write( "(B'A')(AB) = [(B'A')A]B = [B'(A'A)]B = [B'I]B = B'B = I = (AB)'(AB)\r\n" );
document.write( "\r\n" );
document.write( "So\r\n" );
document.write( "\r\n" );
document.write( "(B'A')(AB) = (AB)'(AB)\r\n" );
document.write( "\r\n" );
document.write( "Right multiply both sides by (AB)'\r\n" );
document.write( "\r\n" );
document.write( "[(B'A')(AB)](AB)' = [(AB)'(AB)](AB)'\r\n" );
document.write( "\r\n" );
document.write( "(B'A')[(AB)](AB)'] = (AB)'[(AB)(AB)']\r\n" );
document.write( "\r\n" );
document.write( "(B'A')I = (AB)'I\r\n" );
document.write( "\r\n" );
document.write( "B'A' = (AB)'\r\n" );
document.write( "\r\n" );
document.write( "That's what we were to prove.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );