0 1 0

0 0 1

0 0 0

Then j 3 = 0 and a = λ I+J.

Expand (λ i+j) n = λ ni+nλ {n-1} j+n (n-1)/2λ {n-2} j 2+by binomial theorem. ...

The omitted part is j 3' s project, ..., J n, and these items are all 0, so A n = λ ni+nλ {n-1} j+n (n-1)/2λ {n-2} j 2.