document.write( "Question 762661: why -1*-1=1 \n" ); document.write( "
Algebra.Com's Answer #464094 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The other tutor did not prove it.\r\n" );
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document.write( "We assume that the distributive, identity and inverse principles hold.\r\n" );
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document.write( "First we must prove that (-1)(0) = 0  \r\n" );
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document.write( "[You might already accept that anything times 0 is 0, \r\n" );
document.write( "but even that must be proved!] \r\n" );
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document.write( "Start with: \r\n" );
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document.write( "     (-1)(0)\r\n" );
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document.write( "Since 0 = 0 + 0 we can replace the 0 by (0 + 0):\r\n" );
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document.write( "     (-1)(0) = (-1)(0 + 0)\r\n" );
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document.write( "We use the distributive principle on the right side:\r\n" );
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document.write( "     (-1)(0) = (-1)(0) + (-1)(0)\r\n" );
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document.write( "We subtract (-1)(0) from both sides:\r\n" );
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document.write( "           0 = (-1)(0) \r\n" );
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document.write( "So we have proved that (-1)(0) = 0:\r\n" );
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document.write( "Now start with \r\n" );
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document.write( "(-1)(-1) + (-1)\r\n" );
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document.write( "Since (-1) = (-1)(1), we can substitute (-1)(1) for the second term (-1),\r\n" );
document.write( "and the above becomes:\r\n" );
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document.write( "(-1)(-1) + (-1) = (-1)(-1) + (-1)(1)\r\n" );
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document.write( "We factor (-1) out of both terms:\r\n" );
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document.write( "(-1)(-1) + (-1) = (-1)(-1 + 1)\r\n" );
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document.write( "We know that (-1 + 1) = 0 so we have\r\n" );
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document.write( "(-1)(-1) + (-1) = (-1)(0)\r\n" );
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document.write( "and we have proved above that (-1)(0) = 0, so we have proved\r\n" );
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document.write( "(-1)(-1) + (-1) = 0\r\n" );
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document.write( "and we know that 1 + (-1) = 0, so we replace the 0 on the right\r\n" );
document.write( "by 1 + (-1)\r\n" );
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document.write( "(-1)(-1) + (-1) = 1 + (-1)\r\n" );
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document.write( "We subtract (-1) from both sides:\r\n" );
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document.write( "       (-1)(-1) = 1\r\n" );
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document.write( "Edwin
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