Matrix S^n: Generalizing Matrix Operations

[Nusc]

If I have a matrix

S =

0 0 0 0 ... 0
1 0 0 0 ... 0
0 1 0 0 ... 0
0 0 1 0 ... 0
...
0 0 0 0 .1.0S^2 =0 0 0 0 ... 0
0 0 0 0 ... 0
1 0 0 0 ... 0
0 1 0 0 ... 0
...
0 0 0 0 1.. 0etc.

going in this way S^n would just be the zero matrix.,
How do I generalize S^n of this matrix?

 

[lurflurf]

If S is a lower triangular matrix (n by n), S^n is the zero matrix.
Now prove.