document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=912367>Question 912367</A>: <I><SPAN STYLE=\"word-break: break-all;\"> show that A(adj A)= (adj A)A=(adj A)I </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #553776 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=553776\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I assume that A is a square matrix, then we know<BR>\n" );
document.write( "The inverse of A = adj(A) / det(A) where det is the determinant<BR>\n" );
document.write( "multiply both sides of the = by A and we get<BR>\n" );
document.write( "A*inverse of A = (A*adj(A)) / det(A) and A*inverse of A = (adj(A)*A) / det(A)<BR>\n" );
document.write( "note that * means multiply<BR>\n" );
document.write( "the above implies that<BR>\n" );
document.write( "I = (A*adj(A)) / det(A) and I = (adj(A)*A) / det(A)<BR>\n" );
document.write( "From above, we can say that det(A)I = A*adj(A) and det(A)I = adj(A)*A, then<BR>\n" );
document.write( "A*adj(A) = adj(A)*A= det(A)*I<BR>\n" );
document.write( " </SPAN>\n" );
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