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
~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
a) An example is A = {{{(matrix(2,2, 0,1, 0,0))}}}. Check that {{{A^2}}} = 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.
</pre>