document.write( "Question 1062853: an n x n matrix A is nilpotent if A^r=0 for some positive integer
\n" ); document.write( "(a)give an example of a nonzero nilpotent 2 x 2 matrix
\n" ); document.write( "(b)show that if A is invertible matrix,then A is not nilpotent \n" ); document.write( "

Algebra.Com's Answer #677872 by ikleyn(52797) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "an n x n matrix A is nilpotent if A^r=0 for some positive integer
\n" ); document.write( "(a)give an example of a nonzero nilpotent 2 x 2 matrix
\n" ); document.write( "(b)show that if A is invertible matrix,then A is not nilpotent
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "a) An example is A = . Check that  = 0.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "b) If a matrix A is nilpotent, then det(A) = 0  (determinant).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "   From the other side, if a matrix A is invertible, then its determinant is not zero.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );