document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=8082>Question 8082</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My text(Anton Elem. L.Alg 8th ed) states on pg. 44 \"If A is a square matrix, then we define the nonnegative powers of A to be... A^0 = I\" So a matrix to the zeero power is the identity matrix. Is this true for ALL matricies, including a zero matrix.\r<BR>\n" );
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document.write( "i.e. is [0]^0=[1]? My Ti-92 says it it is, but 0^0 is not 1. Why? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #4467 by </B><A HREF=/tutors/aboutme.mpl?userid=khwang><B>khwang(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=khwang><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=4467\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  It is very good  that you thought of this problem.\r<BR>\n" );
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document.write( " Just like the definition of exponent of numbers, we define<BR>\n" );
document.write( " a^0 = 1 when the base a != 0 (nonzero).<BR>\n" );
document.write( " In other words, 0^0 is undefined. (because a^0 = a/a and a cannot be zero.)\r<BR>\n" );
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document.write( " By the same reason A^0 is undefined when A = 0.<BR>\n" );
document.write( " In other words, A^0 = I for all nonzero square matrix.\r<BR>\n" );
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document.write( " Forget the result from the stupid calculator. It cannot tell you the<BR>\n" );
document.write( " idea hiding inside the beautiful linear algebra.\r<BR>\n" );
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document.write( " Kenny </SPAN>\n" );
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