Jordan Form of Matrix: Find Solution

[talolard]

Homework Statement

find the jordan form of:
$$0 1 0 ... 0$$
$$0 0 1 ... 0$$
$$0 0 0 \ddots$$
$$0 0 0 ... 1$$
$$1 0 0 ... 0$$

Homework Equations

Hint: prove that A^n=ID and then blah blah blah.

The Attempt at a Solution

I assumed that A^n = ID and then i could solve it. i have no idea how to prove that A^n=ID. any help on that would be great.

 

[lanedance]

i'm assuming A is your matrix?

consider any nxn matrix, say B and consider the results of the multiplcation B.A on the columns of B...