SOLUTION: an n x n matrix A is nilpotent if A^r=0 for some positive integer (a)give an example of a nonzero nilpotent 2 x 2 matrix (b)show that if A is invertible matrix,then A is not ni

Question 1062853: an n x n matrix A is nilpotent if A^r=0 for some positive integer
(a)give an example of a nonzero nilpotent 2 x 2 matrix
(b)show that if A is invertible matrix,then A is not nilpotent
Answer by ikleyn(52797) (Show Source): You can put this solution on YOUR website!
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an n x n matrix A is nilpotent if A^r=0 for some positive integer
(a)give an example of a nonzero nilpotent 2 x 2 matrix
(b)show that if A is invertible matrix,then A is not nilpotent
~~~~~~~~~~~~~~~~~~~~~~~~~

a) An example is A = . Check that  = 0.


b) If a matrix A is nilpotent, then det(A) = 0  (determinant).


   From the other side, if a matrix A is invertible, then its determinant is not zero.

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