document.write( "Question 1099395: Please help\r
\n" ); document.write( "\n" ); document.write( "Suppose A, B and AB-I are non-degenerate and have same order. Prove that
\n" ); document.write( "(1) \"A+-+B%5E-1\" is non-degenerate.\r
\n" ); document.write( "\n" ); document.write( "(2) \"%28A+-+B%5E-1%29%5E-1+-+A%5E-1\" is non-degenerate. find the inverse of this matrix. \n" ); document.write( "
Algebra.Com's Answer #713885 by ikleyn(52787)\"\" \"About 
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document.write( "1)  Since the matrix B is non-degenerated, it has the inverse matrix  \"B%5E%28-1%29\".\r\n" );
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document.write( "    Multiply the matrix \"A%2AB-I\" by the matrix \"B%5E%28-1%29\"  on the right. You will get\r\n" );
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document.write( "    \"%28A%2AB-I%29%2AB%5E%28-1%29\" = \"A+-+B%5E%28-1%29\".\r\n" );
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document.write( "    Since both matrices on the left side of the equation are non-degenerated, their product on the right side is non-degenerated, too.\r\n" );
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document.write( "    QED\r\n" );
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