Let N be a nilpontent operator in a vector space of dimensio

Solution

We can do it with the help of eigen value concept.

N is a nilpotent operator that means N^k = 0.

Let p is eigen value of N with eigen vector j.

So,. Nj = pj

N²j = NNj = Npj = pNj = p²j

Same as .... N^kj = p^kj

Now N^k = 0

So,. p^kj = 0

k = 0

So due to 0 eigen value, characteristic equation would be xⁿ.