document.write( "Question 1200894: an n *n matrix A is called nilpotent if, for some positive integer k, A^k = o, where o is the n*n zero matrix. Prove that id A is nilpotent, the det A = 0. \n" ); document.write( "

Algebra.Com's Answer #835120 by ikleyn(52833) $\"\"$ $\"About$

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document.write( "For any matrix A,   = .\r\n" );
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document.write( "If A is a nilpotent matrix, then   = 0;  hence   = 0.\r\n" );
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document.write( "It implies that for nilpotent matrix A   = 0  for some integer k > 0;  hence,  det(A) = 0.    QED\r\n" );
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